Heat corn oil and sesame oil in a large skillet. Add carrots, green bell pepper, and onion; cook and stir until softened, about 5 minutes. Stir in soy sauce, sake, mirin, sugar, and fish soup stock. Mix in garlic and ginger. Let cool, 5 to 10 minutes.
Mix turkey, pork, and eggs together in a large bowl until blended. Stir in cooled carrot mixture and bread crumbs until well combined. Press evenly into a loaf pan.
Bake in the preheated oven until browned, about 30 minutes. Increase oven temperature to 400 degrees F (200 degrees C); continue baking until an instant-read thermometer inserted into the center reads at least 160 degrees F (70 degrees C), about 30 minutes more.