Brown the ground beef in a large skillet over medium-high heat. Flip and push to one side of the skillet. Add the olive oil and onion, celery, and carrot. Stir everything together, breaking the beef apart.
Once fully cooked, add the flour, salt garlic powder, and pepper. Stir until no flour is visible. Add the tomato paste and cook until fragrant.
Add the broth, vinegar, Worcestershire, thyme, and bay leaves. Bring up to a boil before reducing the heat to a medium-low simmer. Cook for 10-15 minutes, stirring occasionally, until the meat mixture is thick like a gravy or bolognese.
Transfer the mixture to a baking dish and place in the freezer while you microwave the cauliflower mash. (I used a smaller 10" x 6" dish but an 8" x 8" or larger will work.)
Top the mixture with the cauliflower mash, followed by the grated parmesan. Drizzle the 1/2 tablespoon of olive oil over the top. If you're using a smaller dish, you may want to place it on a sheet pan to catch any drippings.
Bake at 350ºF for 35-45 minutes until the top is golden brown. Top with fresh parsley and serve.