Thanks in advance for any help..

I am trying to set up new 240 v baseboard heating in my attic

My questions is can I put it through 2 different single pole breakers - each for every phase?

Heater = 240v / 1500w
breakers = 15A

And what can be wrong? (technically - this is not a code question)

No, you need a 2-pole breaker with a bar between them, so if one side trips the other one will too.

To really answer your question: Yes you could, but DON'T. It creates a fire hazzard. You will either end up with 0V or 240 Volts depending on what breakers you chose. The 120 V sides will add or subtract depending on the phase.

Crazy to try, when one leg trips the other must also or you will always have a hot leg when one trips out and that could cause fires & DEATH.