**Cook the Pasta:**
Preheat the oven to 375°F (190°C). Cook the jumbo pasta shells in salted water until al dente, according to package instructions. Drain and set aside to cool slightly.
**Make the Alfredo Sauce:**
In a saucepan over medium heat, melt the butter and sauté the garlic for 1-2 minutes until fragrant. Add the heavy cream and bring to a simmer. Gradually whisk in the Parmesan cheese until smooth. Season with black pepper and a pinch of nutmeg, if desired. Remove from heat and set aside.
**Prepare the Filling:**
In a mixing bowl, combine shredded chicken, chopped broccoli, ricotta, mozzarella, Parmesan, egg, garlic powder, onion powder, and Italian seasoning. Mix until well combined.
**Stuff the Shells:**
Spoon or pipe the filling into each cooked pasta shell. Arrange the stuffed shells in a greased baking dish in a single layer.
**Assemble the Dish:**
Pour the Alfredo sauce evenly over the stuffed shells. Sprinkle the top with shredded mozzarella and grated Parmesan.
**Bake:**
Cover the dish with foil and bake for 20 minutes. Remove the foil and bake for an additional 10-15 minutes, or until the cheese is melted and bubbly.
**Serve:**
Garnish with fresh parsley, if desired, and serve hot.