Heat canola oil in a skillet over medium heat; add onion, jalapeno, and garlic. Cook until onions are translucent, 10 to 12 minutes. Cool to room temperature, about 15 minutes.
Mix the onion mixture, ground turkey, teriyaki sauce, and soy sauce together in a bowl using a fork. Chop half the peach and mix gently into the bowl with the turkey mixture. Season with salt and pepper. Form into 4 patties.
Preheat grill for medium heat and lightly oil the grate.
Cook turkey burgers on the preheated grill until no longer pink in the center and the juices run clear, about 4 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Combine endive and spring mix in a bowl. Top with avocado, Gorgonzola cheese, and bacon. Serve alongside turkey burgers.
