Preheat the oven to 375°F.
Sauté the mushrooms: In a pan over medium heat, add 6 oz button mushrooms, 1 tbsp olive oil, 1 tsp minced garlic, 1 tsp fresh thyme leaves, and 1 oz chopped onion. Cook for 3 minutes, stirring constantly.
Sauté the beef: In the same pan, add 8 oz ground beef, 1/4 tsp black pepper, 1 tsp Italian seasoning, 1 tsp paprika, and 2 1/2 tsp Dijon mustard. Stir and cook for another 5 minutes over medium heat. Once cooked, transfer to a plate and set aside.
Make the roux: In a medium saucepan over low heat, add 1 tbsp unsalted butter and 4 tbsp all-purpose flour. Stir constantly until combined.
Make the white sauce: In the same saucepan, add 3/4 cup water, 1 cup whole milk, 2 tbsp heavy cream, 1/2 tsp garlic powder, and 1/2 tsp salt. Whisk constantly and cook over high heat. Once the sauce begins to boil, reduce the heat to medium and simmer for another 5 minutes, stirring occasionally. Turn off the heat when done.
Layer the lasagna: Spread 1/2 cup homemade tomato sauce on the bottom of a baking dish (we used a 7.5x7.5x2-inch dish). Then layer 4 lasagna sheets on top of the sauce. Spread an even layer of all the ingredients in this following order: half the sautéed ground beef, 8 oz riced cauliflower, half the white sauce, 1 tbsp chopped basil, 1/2 cup homemade tomato sauce, 4 lasagna sheets, 8 oz riced cauliflower, half the white sauce, 1 tbsp chopped basil, and 2 oz shredded mozzarella cheese.
Bake the lasagna: Put the baking dish into the preheated oven on the bottom rack and bake for 45 minutes.
Garnish and serve: Remove the lasagna from the oven. Allow to cool at least 10 minutes. Sprinkle with chopped parsley to garnish, cut into 4 portions, and serve.