Mince the onion and the carrot in a food processor.
Add the pressed tofu to a large bowl with the teriyaki and soy sauce. Marinate for 10 minutes.
Coat the bottom of a pan with oil and heat to medium-high. Add minced carrot, onion, tofu and any excess sauce to the skillet.
Using a ladle, crush the tofu until it's crumbly. Constantly flip until the ground tofu mixture is thoroughly cooked. When finished cooking, let cool.
Once the mixture has cooled, apply 1 tablespoon of the mixture in the center of a wonton wrap. Fold the wrapper in half to form a triangle using a small amount of water to seal the tofu mixture in. Repeat as many times as necessary.
On medium-high heat, fry the wontons until both sides are lightly browned, set aside the finished wontons to cool.