Έχοντας βάλει τη λαδόκολλα στο ταψί, άνοιξα τη ζύμη με τον πλάστη.

It means having put or, more naturally in English, after putting / once I had put.

In this sentence, Έχοντας βάλει τη λαδόκολλα στο ταψί is an introductory clause that sets up the action in the main clause. So the sentence means:

After putting the baking paper in the tray, I rolled out the dough with the rolling pin.

It is a common Modern Greek way to express having done something:

• έχοντας = the -οντας participle form of έχω
• βάλει = the form used after έχω in perfect-type constructions, as in έχω βάλει

So:

• έχω βάλει = I have put
• έχοντας βάλει = having put

This whole phrase functions adverbially, describing the circumstances before the main action.

Because after έχοντας, Greek does not use a normal finite past-tense verb like έβαλα.

• έβαλα = I put / I placed
• βάλει = the form used with έχω, as in έχω βάλει

So:

• έχοντας βάλει = correct
• έχοντας έβαλα = incorrect

A good way to think of it is that έχοντας needs a non-finite companion form, not a normal past tense.

Yes. The order is:

1. I put the baking paper in the tray
2. I rolled out the dough

So Έχοντας βάλει... clearly marks an action completed before άνοιξα.

That is why English often translates it as after putting or having put.

It is the same subject as the main verb άνοιξα.

Here, άνοιξα means I rolled out, so the understood subject is I. That means:

• I put the baking paper
• I rolled out the dough

This is very common in Greek: the subject does not need to be stated with εγώ, because the verb ending already shows the person.

Because Greek is a pro-drop language. The verb ending usually tells you who the subject is.

Here:

• άνοιξα = I rolled out

So εγώ is unnecessary unless you want emphasis or contrast.

For example:

• Άνοιξα τη ζύμη = I rolled out the dough
• Εγώ άνοιξα τη ζύμη = I rolled out the dough / It was I who rolled out the dough

The second version is more emphatic.

Literally, ανοίγω often means open, but in cooking it very often means roll out or spread out, especially with dough.

So:

• ανοίγω τη ζύμη = I roll out the dough

This is a normal cooking expression in Greek. It does not sound strange to a Greek speaker.

Because άνοιξα is the aorist, which presents the action as a completed whole.

Here the sentence describes completed steps in a sequence:

• I put the paper in the tray
• I rolled out the dough

So άνοιξα fits perfectly.

By contrast, άνοιγα is the imperfect, which would suggest:

• an ongoing action: I was rolling out
• a repeated/habitual action: I used to roll out

That would not fit this sentence as well.

στο is a contraction of σε + το.

So:

• σε = in / on / to / into, depending on context
• το ταψί = the tray / baking pan

Therefore:

• στο ταψί = in the tray, on the tray, or into the tray

In this cooking context, English would usually say something like in the baking tray or on the tray, depending on how you imagine the paper being placed.

λαδόκολλα means baking paper, greaseproof paper, or parchment paper.

It is a very common kitchen word in Greek.

In the sentence:

• τη λαδόκολλα = the baking paper

It is in the accusative because it is the direct object of βάλει.

Because Greek marks case on the article.

Here is what is happening:

• τη λαδόκολλα → accusative feminine singular, because it is the direct object of βάλει
• το ταψί inside στο → neuter singular after σε
• τη ζύμη → accusative feminine singular, because it is the direct object of άνοιξα
• τον πλάστη → accusative masculine singular after με

English articles do not change like this, but Greek articles do.

Because Greek uses the definite article more often than English does.

In a sentence like this, the article sounds very natural with concrete, specific things:

• τη λαδόκολλα
• το ταψί
• τη ζύμη
• τον πλάστη

English often omits articles more freely in recipe-style language, but Greek usually keeps them in normal full sentences.

Because the final -ν of the feminine accusative article is often dropped before certain consonants.

Since λαδόκολλα begins with λ, the normal form here is:

• τη λαδόκολλα

Similarly:

• τη ζύμη

You will often see την kept before vowels and certain consonants, but before λ dropping the -ν is standard and very common.

It means with the rolling pin.

Here με expresses the instrument used to do the action.

So:

• άνοιξα τη ζύμη με τον πλάστη = I rolled out the dough with the rolling pin

Modern Greek does not have a separate instrumental case, so it normally uses με + accusative for this meaning.

πλάστης means rolling pin.

In the sentence it appears as:

• τον πλάστη

That is the masculine accusative singular form with the article, because it comes after με.

It is natural, but Έχοντας βάλει... sounds a little more written or carefully phrased than the most everyday spoken version.

A more conversational way to say the same thing would be:

• Αφού έβαλα τη λαδόκολλα στο ταψί, άνοιξα τη ζύμη με τον πλάστη.
• Έβαλα τη λαδόκολλα στο ταψί και μετά άνοιξα τη ζύμη με τον πλάστη.

The original sentence is still perfectly good Greek.

Yes, Greek word order is fairly flexible, but the original order is very natural.

The sentence begins with the introductory participial phrase:

• Έχοντας βάλει τη λαδόκολλα στο ταψί, ...

Then comes the main clause:

• άνοιξα τη ζύμη με τον πλάστη

This order is clear and elegant because it presents the earlier action first. The comma helps separate the introductory phrase from the main action.