01 - Preheat the oven to 400°F.
02 - Bring a large pot of salted water to a boil. Add cauliflower florets and cook until very tender, approximately 10 to 12 minutes. Drain thoroughly.
03 - Heat olive oil in a large skillet over medium heat. Add diced onion, minced garlic, diced carrots, and diced celery. Sauté until softened, about 5 minutes.
04 - Add ground beef to the skillet. Cook, breaking it up with a spoon, until fully browned, about 6 to 8 minutes.
05 - Stir in tomato paste, beef broth, Worcestershire sauce, dried thyme, and dried rosemary. Simmer for 5 to 7 minutes until mixture thickens slightly.
06 - Stir in frozen peas. Season with salt and black pepper, then simmer for 2 additional minutes. Remove from heat.
07 - In a food processor or with a hand masher, blend cooked cauliflower with butter and milk until very smooth. Season with salt and white pepper.
08 - Spread the beef mixture evenly into a 9x13-inch baking dish. Top with the cauliflower mash, smoothing the surface with a spatula.
09 - Sprinkle grated Parmesan cheese over the top, if using.
10 - Bake in the preheated oven for 20 minutes or until the topping is lightly golden and the filling is bubbling. Allow to rest for 5 minutes before serving.