My way of losing weight recently has been a pretty flexible low carb diet with mct oil coffee. I lost about nine kilograms and am now maintaining my current weight. You can learn the science on YouTube from people like Dr Jason Fung, Dr Gundry and Dr Berg (although he's a chiropractor, the other two are real doctors). I don't know if it is safe or works for everyone, though.
1100 calories is too low to not feel like binging. I aimed for about 1400-1600 calories a day, it's easier to be consistent that way. A low carb diet affects working out, though. I need to eat something carb heavy before going for a walk etc, like half a banana or a slice of bread, just to have some glucose in my body for that. Muscle cells can only burn glucose.