Step 1 - Prepare Mashed Cauliflower for Topping
Place cauliflower in a large pot covered with water. Bring to a boil. Reduce to a gentle boil and cook with lid on for 8 - 10 minutes. Cauliflower should be tender but not mushy. Remove from heat. Drain well. Put the cauliflower back in pot with lid on and let stand for 5 minutes. This ensures the cauliflower doesn't get watery. Don't skip this step.
Place cooked cauliflower in the food processor with butter and spices. Pulse until it becomes whipped/consistency of mashed potatoes (you might want to do it in two batches depending on your food processor size). Instead of butter I have also used plain Greek Yogurt or cream cheese - its pretty versatile so use what you've got. Set aside.
Step 2 - Prepare Base for Pie
Brown the ground beef over medium heat. In a separate pan, fry the oil, garlic, onion and carrots over medium heat until softened. About 3 -5 minutes. Add celery and mushrooms and cook for one additional minute. Add browned ground beef, salt, Worcestershire, broth, soy sauce, tomato paste and parsley to the mixture. Simmer over medium heat for about 15 minutes until cooked through and some of the juice has cooked off (so its not runny).
Add frozen peas in for the last 10 minutes or so. I didn't need to thicken mine but if your beef was not lean you may have to thicken with guar gum or another thickener or continue simmering until thickened to your liking.
Step 3 - Assemble and Bake Pie
Preheat the oven to 350 degrees. Spread the beef mixture into a 9 x 13 casserole dish. Top with mashed cauliflower. I dolloped it out evenly over the top and then smoothed it down with the back of a spoon to evenly distribute it over the top. Sprinkle with Mozzarella cheese, Parmesan cheese and a dash of Paprika.
Bake in the oven for 45 minutes until bubbling and cheese is cooked. Broil cheese for a couple of minutes if it doesn't crisp up - it will depend on the type of cheese you use. Let stand for 5 - 10 minutes before slicing and serving.