01 - Set oven temperature to 400°F.
02 - Boil salted water in a large pot, add cauliflower florets and cook until tender, about 10 to 12 minutes. Drain thoroughly.
03 - Heat olive oil in a skillet over medium heat. Add diced onion, garlic, carrots, and celery, cooking until softened, about 5 minutes.
04 - In the same skillet, add ground beef, breaking it up with a spoon, and cook until browned, approximately 6 to 8 minutes.
05 - Incorporate tomato paste, beef broth, Worcestershire sauce, thyme, and rosemary. Reduce heat and simmer for 5 to 7 minutes until slightly thickened.
06 - Stir frozen peas into the beef mixture and season with salt and black pepper. Simmer for an additional 2 minutes then remove from heat.
07 - Blend the cooked cauliflower with butter and milk using a food processor or hand masher until smooth. Season with salt and white pepper.
08 - Evenly spread the beef mixture in a 9x13-inch baking dish. Smooth the cauliflower mash atop the beef layer.
09 - Sprinkle grated Parmesan cheese over the cauliflower mash if desired.
10 - Bake for 20 minutes or until the topping is lightly golden and the filling bubbles. Allow to rest for 5 minutes before serving.