Preheat the oven to 400°F.
Heat olive oil in a large skillet, then add the onions and sauté.
1 tablespoon olive oil, 1 large onion
Once the onions are translucent, add the ground meat. Season with salt, pepper, and thyme.
1 pound ground chicken or turkey, Kosher salt, Freshly ground black pepper, 3 to 4 sprigs fresh thyme leaves
Cook until the meat is no longer pink, then transfer to a flat surface lined with paper towels to drain.
Return the meat to the skillet, then add the butter along with the frozen peas and carrots. Once vegetables begin to thaw, sprinkle with flour and stir well.
1 tablespoon butter, 16 ounces frozen peas and carrots, 2 tablespoons all-purpose or gluten-free flour
Add the tomato paste, slightly more than half the beef stock, and Worcestershire sauce. Stir well.
2 tablespoons tomato paste, 1¼ cup beef, chicken or vegetable stock/broth, 2 tablespoons Worcestershire sauce
Let the mixture reduce slightly, then add the remaining beef stock.
1¼ cup beef, chicken or vegetable stock/broth
Reduce again until you have a thick gravy. Taste and add more salt and pepper, if necessary.
Spray a 9x13-inch baking dish with nonstick cooking spray. Add the meat mixture, then spread the mashed potatoes or cauliflower on top.
6 cups mashed potatoes or mashed cauliflower
Brush with top with the beaten egg, then sprinkle with cheese.
1 large egg, ¼ cup grated Parmesan cheese
Place the baking dish on a cookie sheet lined with foil to catch any drips. Then, place everything in the oven and bake for about 30 minutes or until the top starts to brown.
Remove from the oven and allow the dish to rest for about 10 minutes before serving.