Η γιαγιά μου βάζει λίγο σαλάμι πάνω στο παξιμάδι, αλλά εγώ το προτιμώ μόνο με ντομάτα.

In Greek, the definite article is normally used with possessive expressions like η γιαγιά μου.

So:

• η γιαγιά μου = my grandmother
• literally, it looks like the grandmother of mine

This is completely normal Greek. The article is not extra emphasis here; it is just the standard way to say it.

The unstressed possessive pronouns in Greek usually come after the noun:

• η γιαγιά μου = my grandmother
• το σπίτι μου = my house
• ο φίλος μου = my friend

So an English speaker has to get used to the pattern noun + μου/σου/του/της/μας/σας/τους.

Βάζει is the 3rd person singular present tense of βάζω, meaning to put, to place, and in food contexts often to put on / add / spread.

Here it means something like:

• she puts
• she adds
• she puts on top

So Η γιαγιά μου βάζει... means My grandmother puts/adds...

Here λίγο means a little or some.

With food words, Greek often uses λίγο + noun very naturally:

• λίγο σαλάμι = a little / some salami
• λίγο τυρί = a little / some cheese

Even though salami can be counted in slices, Greek often treats foods like this as a quantity or substance. If you wanted to be more specific, you could say something like λίγες φέτες σαλάμι = a few slices of salami.

Πάνω στο παξιμάδι means on the paximadi / on top of the rusk.

A useful thing here is:

• στο = σε + το

So:

• σε το becomes στο

And πάνω σε means on, onto, or on top of. In everyday Greek, πάνω στο is extremely common.

Yes, Greek often drops subject pronouns because the verb ending already shows who the subject is.

So Greek could simply say:

• αλλά προτιμώ...

But here εγώ is included for contrast:

• but I prefer it...

The sentence contrasts my grandmother's preference/habit with my own:

• Η γιαγιά μου... αλλά εγώ...
• My grandmother..., but I...

So εγώ adds emphasis: as for me / I, on the other hand.

Το means it, and it refers to the thing just mentioned — most naturally the παξιμάδι or the prepared snack as a whole.

Why το?

• because παξιμάδι is neuter
• the weak object pronoun for a neuter singular direct object is το

So:

• το προτιμώ = I prefer it

This is a very common Greek structure: instead of repeating the noun, Greek uses a short object pronoun.

Because προτιμώ means I prefer, and it normally takes an object:

• προτιμώ το παξιμάδι
• I prefer the paximadi

Once the object is already known, Greek often replaces it with a pronoun:

• το προτιμώ
• I prefer it

So the το is not optional if you want to say I prefer it rather than just I prefer.

Because here ντομάτα is being used in a general ingredient sense:

• μόνο με ντομάτα = only with tomato

Greek often leaves out the article after με when talking about what something contains or is served with:

• με τυρί = with cheese
• με μέλι = with honey
• με ντομάτα = with tomato

If you said με τη ντομάτα, it would sound more like a specific tomato or a more definite, context-specific reference.

Greek word order is more flexible than English word order, but the version here sounds natural and neutral.

For example:

• Η γιαγιά μου βάζει λίγο σαλάμι πάνω στο παξιμάδι is the normal way to present the information.
• αλλά εγώ το προτιμώ μόνο με ντομάτα puts the focus naturally on my preference.

The position of μόνο is also important:

• μόνο με ντομάτα = only with tomato

That means the limitation applies to the ingredient phrase.

Several common case patterns appear here:

• η γιαγιά μου: η γιαγιά is the subject, so it is in the nominative
• λίγο σαλάμι: σαλάμι is the direct object of βάζει, so it is in the accusative
• στο παξιμάδι: after σε (here contracted as στο), Greek uses the accusative
• το in το προτιμώ: direct object pronoun, so also accusative
• με ντομάτα: με takes the accusative

A tricky point is that some of these nouns look the same in nominative and accusative, especially neuter nouns like σαλάμι and παξιμάδι.

Yes. Βάζω is a very broad everyday verb, and Greek uses it a lot in food contexts.

Depending on the situation, it can mean:

• put
• add
• serve with
• sometimes even something close to spread or lay on top

So in this sentence, βάζει λίγο σαλάμι πάνω στο παξιμάδι is perfectly natural Greek for putting some salami on the bread/rusk.