Cook chopped bell peppers and onion on griddle until translucent, about 10 minutes. Remove and set aside.
Season steak with salt, pepper, and garlic. Cook on griddle for 6-8 minutes.
Combine soy sauce, brown sugar, oyster sauce, rice wine vinegar, sesame oil, garlic paste, ginger paste, red pepper flakes, and water to make sauce.
Add veggies back to the griddle with the steak, pour in sauce, and cook until caramelized. Remove mixture from griddle.
Clean griddle surface with water and add avocado oil.
Place tortilla on griddle, warm for 60-90 seconds, flip, and add cheese, pepper steak mixture, chipotle mayo or sour cream, and more cheese. Fold into quesadilla.
Toast until golden brown, cut, and serve.