Preheat and prep: Heat oven to 375°F (190°C). Grease a 9x13-inch baking dish.
Cook the pasta: Bring a large pot of salted water to a boil. Cook gluten-free pasta 2 minutes less than package directions for al dente.
In the last 2 minutes of cooking, add the broccoli florets to blanch. Drain and set aside.
Cook the chicken: Heat olive oil in a large skillet over medium-high. Season chicken with 1/2 teaspoon salt, 1/4 teaspoon pepper, and Italian seasoning.
Sauté 5–7 minutes until cooked through and lightly browned. Transfer to a plate.
Make the Alfredo base: In the same skillet over medium heat, melt butter. Add garlic and cook 30 seconds until fragrant.
Whisk in gluten-free flour and cook 1 minute to form a roux.
Build the sauce: Slowly whisk in milk, then cream and broth. Simmer 3–5 minutes, whisking, until thick enough to coat a spoon. Season with remaining salt and pepper.
Stir in Parmesan and 1/2 cup mozzarella until smooth.
Add brightness: Stir in lemon zest, a teaspoon of lemon juice, basil, and red pepper flakes if using. Taste and adjust salt, pepper, and lemon.
Combine: In a large bowl, mix pasta, broccoli, chicken, and the Alfredo sauce. Transfer to the prepared baking dish and spread evenly.
Top and bake: Sprinkle remaining 1/2 cup mozzarella and a little extra Parmesan over the top.
Bake 18–22 minutes, until bubbly around the edges.
Brown the top (optional): Broil 1–2 minutes for a golden crust. Watch closely.
Rest and serve: Let sit 5–10 minutes to set. Garnish with fresh basil and an extra squeeze of lemon if you like.