Preheat your oven to 375°F (190°C).

To prepare the topping, steam or boil the cauliflower florets until they are very tender, about 10-15 minutes. Drain thoroughly.

Transfer the cooked cauliflower to a large bowl. Mash with milk, butter, salt, and pepper until smooth and creamy. Stir in the grated Parmesan cheese if you are using it. Set aside.

For the filling, heat olive oil in a large skillet or Dutch oven over medium-high heat. Add the lean ground beef and cook, breaking it up with a spoon, until it is thoroughly browned. Drain any excess fat.

Add the chopped onion, diced carrots, and diced celery to the skillet with the beef. Cook for 5-7 minutes, stirring occasionally, until the vegetables begin to soften.

Stir in the minced garlic and cook for another minute until fragrant.

Add the tomato paste to the skillet and cook for 1 minute, stirring constantly, to deepen its flavor.

Pour in the beef broth and bring the mixture to a simmer, scraping up any browned bits from the bottom of the pan. Stir in the dried thyme.

Reduce the heat to medium-low. Stir in the frozen peas and frozen corn. Season the filling with salt and black pepper to taste. Simmer for about 5 minutes, allowing the sauce to thicken slightly.

Pour the hot filling into a 9x13 inch baking dish (or 6 individual oven-safe ramekins). Carefully spread the mashed cauliflower topping evenly over the filling, ensuring it covers the meat mixture completely.

Bake in the preheated oven for 20-25 minutes, or until the filling is bubbly and the cauliflower topping is lightly golden brown. For a deeper golden crust, you can broil for the last 2-3 minutes, watching carefully to prevent burning.

Remove from the oven and let stand for 5-10 minutes before serving, allowing the pie to set.