Ben kahveye biraz tarçın koymadan edemiyorum.

Yes. Turkish verbs usually show the subject, so edemiyorum already means I can’t.

That means ben is optional here. It is often added for:

• emphasis
• contrast
• a more personal tone

So both of these are possible:

• Ben kahveye biraz tarçın koymadan edemiyorum.
• Kahveye biraz tarçın koymadan edemiyorum.

The version with ben can sound a bit like as for me... or I personally....

Kahveye is the dative form of kahve, using -e / -a.

Here, the coffee is the target/destination of the action:

• tarçın koymak = to put cinnamon
• kahveye koymak = to put it into the coffee

So the sentence structure is basically:

• [thing being added]: biraz tarçın
• [where it is added]: kahveye

Compare:

• Şorbaya tuz koydum. = I put salt in the soup.
• Çaya şeker koyuyor. = He/She puts sugar in the tea.

So kahveye means something like into the coffee / in coffee.

Biraz means a little or some.

In biraz tarçın, it tells you the amount:

• tarçın = cinnamon
• biraz tarçın = a little cinnamon / some cinnamon

This is very normal Turkish word order: the quantity word comes before the noun.

You will often see similar phrases like:

• biraz su = a little water
• biraz şeker = a little sugar
• biraz zaman = a little time

Because tarçın here is an indefinite, non-specific object.

In Turkish, a direct object often appears without the accusative ending when it is:

• indefinite
• non-specific
• more like some X rather than that specific X

So:

• biraz tarçın koymak = to put some cinnamon
• tarçını koymak would suggest the cinnamon, a specific known cinnamon

That is why bare tarçın is natural here.

Koymadan means without putting.

It comes from the verb koymak = to put, place, add.

The ending -madan / -meden is a very common Turkish form meaning:

• without doing
• before doing in some contexts, but its core idea is without doing

So:

• koymadan = without putting
• gitmeden = without going
• yemeden = without eating
• bakmadan = without looking

It is best to learn -madan / -meden as a single useful pattern.

This is a very important Turkish pattern:

-madan / -meden edememek

It means:

• to be unable to refrain from doing
• to not be able to help doing
• to always end up doing

So koymadan edemiyorum does not simply mean I cannot do without putting in a fully literal English way. As a whole, it means something like:

• I can’t help putting...
• I just have to put...
• I can’t resist putting...

This is a fixed and very common structure in Turkish.

Other examples:

• Gülmeden edemiyorum. = I can’t help laughing.
• Bakmadan edemedim. = I couldn’t help looking.
• Sormadan edemeyeceğim. = I won’t be able to stop myself from asking.

Not in the way an English learner might first think.

You may notice:

• -madan = without doing
• edemiyorum = I can’t do

So it looks negative twice. But in Turkish, this is a normal idiomatic structure, not a confusing logical double negative.

As a whole, -madan edememek expresses:

• can’t help doing
• can’t refrain from doing

So you should learn it as one unit of meaning rather than trying to translate each negative piece separately every time.

It comes from the verb etmek = to do.

In this pattern, Turkish uses edememek / edemiyorum as part of the fixed expression:

• -madan edememek

Also, notice the sound change:

• dictionary form: etmek
• in many conjugated forms: ed-
• so: ediyor, edemiyor, etc.

That is why you see:

• edemiyorum not
• etemiyorum

So in this sentence, edemiyorum is not carrying its full simple meaning of I cannot do by itself. It is part of the idiom.

Because Turkish present continuous forms in -iyor are used more broadly than English am/is/are doing.

In Turkish, -iyor can express:

• something happening now
• a repeated behavior
• a habitual tendency
• a current personal pattern

So edemiyorum here can naturally mean:

• I can’t help it
• I always end up doing this
• This is what I tend to do

That is completely normal Turkish usage.

Turkish word order is fairly flexible.

The version you have is natural, but other versions are possible depending on emphasis:

• Ben kahveye biraz tarçın koymadan edemiyorum.
• Kahveye biraz tarçın koymadan edemiyorum.
• Biraz tarçın koymadan kahve içemem would be a different sentence, but it shows how Turkish can shift things around for focus.

In general:

• the verb tends to come at the end
• the element right before the verb is often strongly connected to it or more focused

Here, biraz tarçın koymadan stays together because it forms the action phrase.

Often, yes—if the speaker specifically means my coffee.

Compare:

• kahveye = to coffee / into coffee / in coffee generally
• kahveme = to my coffee

So:

• Kahveye biraz tarçın koymadan edemiyorum. can sound more general, like I can’t help adding a little cinnamon to coffee.
• Kahveme biraz tarçın koymadan edemiyorum. sounds more specifically like I can’t help adding a little cinnamon to my coffee.

Both are possible; they just focus slightly differently.

Yes, absolutely. It is a very productive and useful pattern.

A few common examples:

• Gülmeden edemiyorum. = I can’t help laughing.
• Merak etmeden edemiyorum. = I can’t help wondering.
• Sormadan edemedi. = He/She couldn’t help asking.
• Bakmadan edemem. = I can’t help looking.

So if you understand koymadan edemiyorum, you are learning a pattern that works far beyond this one sentence.