01 - Preheat the oven to 400°F.
02 - Bring a large pot of salted water to a boil. Add cauliflower florets and cook until tender, about 10 to 12 minutes. Drain thoroughly.
03 - While cauliflower cooks, heat olive oil in a large skillet over medium heat. Add onion, garlic, carrots, and celery. Sauté until softened, about 5 minutes.
04 - Add ground beef to the skillet. Break up with a spoon and cook until browned and cooked through, about 6 to 8 minutes.
05 - Stir in tomato paste, beef broth, Worcestershire sauce, thyme, and rosemary. Simmer until slightly thickened, about 5 to 7 minutes.
06 - Mix in frozen peas, season with salt and black pepper, and simmer for 2 more minutes. Remove from heat.
07 - Blend cooked cauliflower with butter and milk in a food processor or mash by hand until smooth. Season with salt and white pepper.
08 - Spread beef mixture evenly in a 9x13 inch baking dish. Top with cauliflower mash and smooth the surface with a spatula.
09 - Sprinkle Parmesan cheese evenly over the mash if using.
10 - Bake in the preheated oven for 20 minutes, or until the topping is lightly golden and the filling is bubbling. Let rest for 5 minutes before serving.