Heat a large pot with 2” of water and add cauliflower florets to a steamer basket. Cook until tender, about 8-10 minutes.
While the cauliflower is cooking, heat a large skillet and add avocado oil or butter. Add onions, carrots, and celery. Cook for 3-5 minutes until fragrant. Add ground meat, 1 teaspoon salt, ½ teaspoon pepper, rosemary, and thyme. Cook until browned.
Preheat oven to 350 F degrees and coat a 9×13 baking dish with non-stick spray or butter.
Add ½ cup broth, Worcestershire, and tomato paste to meat/veggie mixture. Stir until well combined. Turn off heat and let cool slightly to thicken.
When cauliflower is tender, turn the heat off and drain. Add cooked florets, heavy cream, cream cheese, ½ teaspoon salt, and ¼ teaspoon pepper to a high-speed blender or food processor and blend on high until smooth. Adjust seasoning to taste.
Add meat/veggie mixture to the bottom of the baking dish. Pour cauliflower mash over the top of the meat and smooth out to the edges. Sprinkle on the parmesan cheese and bake for 25-30 minutes until edges begin to brown.