Preheat the oven to 375°F. Line a baking sheet with aluminum foil, and spray with cooking spray. Set aside.
Add the olive oil to a nonstick skillet over medium-high heat. When oil is hot, add the onion, carrot, and garlic, and saute for about 5 to 7 minutes, stirring occasionally until softened. Remove from the heat and allow to cool.
In a large mixing bowl add the ground turkey, cooled onion-carrot mixture, egg, breadcrumbs, milk or broth, Worcestershire sauce, ketchup, salt, pepper, and thyme. Mix together gently with your hands until ingredients are fully incorporated, but do not over-mix.
Shape the mixture into a free-from rectangular loaf shape on the prepared pan, measuring approximately 9-by-4-inches. Bake for about 50 minutes, or until an instant read thermometer inserted into the center of the loaf reads 165°F. Rest for 5 minutes before slicing and serving.
Meanwhile, make the onion gravy. In a medium saucepan heat the oil or butter over medium-low heat. Add the onions and a big pinch of salt. Cover the onions and cook for about 10 minutes, stirring occasionally, until the onions sweat and are softened.
Uncover and continue to cook for another few minutes, then dust with the flour, stirring to coat. Add the broth a little at a time, whisking thoroughly between additions to ensure a smooth gravy without lumps. Raise the heat to high. Add the Worcestershire sauce, thyme, and salt and pepper.
When the gravy starts bubbling, lower the heat to medium, and continue to cook for about 5 to 10 minutes until thick and flavorful.
Serve the meatloaf with mashed potatoes, and gravy drizzled over the top of both the meatloaf and potatoes.