My goal is to make something like those from the MIT, or if it is possible, even better.
It is possible and likely.
The avr based esc is practically in the public domain and you can find everywhere. Many firms offer public domain mcu-based BLDC controller code that you can adapted to AVR, or any other chips you wish to use.
Having said that, bldc control is actually quite complicated. Without good understanding of analog / digital electronics, I suggest that you don't set too high of an expectation for yourself.