Preheat the oven to 375°F (190°C).
Cook pasta according to package instructions until al dente. Drain and set aside.
Lightly steam broccoli florets until just tender.
In a large skillet, melt butter over medium heat and sauté garlic until fragrant, about 1 minute.
Add heavy cream and bring to a gentle simmer.
Stir in Parmesan cheese, salt, black pepper, and nutmeg until the sauce is smooth and thickened.
Add the cooked pasta and steamed broccoli to the sauce, mixing until evenly coated.
Transfer the pasta and sauce mixture to a greased 9x13-inch baking dish.
Sprinkle shredded mozzarella evenly over the top.
If using, mix breadcrumbs with olive oil and sprinkle over the cheese for a crunchy topping.
Bake uncovered for 25–30 minutes, until the cheese is melted and golden brown.
Remove from oven and allow to cool for 5 minutes before serving.