Heat the oil in a medium skillet over medium-high heat. Add the onions and cook until they are translucent. Add the garlic and cook until the onions are soft and golden, 5 minutes, stirring often.
Add the turkey and cook, breaking it up with a wooden spoon, until it all looks white, 5 minutes. Add the tomatoes with their liquid, the tomato sauce, stevia, molasses, soy sauce, Worcestershire, and hot sauce. Simmer, until the sauce thickens enough to coat the turkey moistly, about 5 minutes. Mix in the vegetables and cook until they are heated through.
Toast the split hamburger buns, if desired. Place the bottom of a bun on each of 4 plates. Spoon one-fourth of the turkey mixture over the bun. Cover with the bun top, and serve.