Preheat oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.

Bring a large pot of salted water to a boil. Add penne pasta and cook according to package directions until al dente. During the last 3 minutes of cooking, add the broccoli florets to the pasta water to blanch. Drain the pasta and broccoli well, then set aside.

While the pasta cooks, heat 1 tbsp olive oil in a large skillet or Dutch oven over medium-high heat. Season chicken cubes with 1/2 tsp salt and 1/4 tsp pepper. Add chicken to the skillet and cook for 5-7 minutes, stirring occasionally, until browned and cooked through. Remove chicken from the skillet and set aside.

Reduce heat to medium. Add 4 tbsp butter to the same skillet. Once melted, add flour and whisk constantly for 1-2 minutes until a light golden roux forms.

Gradually whisk in the warm milk, a little at a time, to avoid lumps. Continue whisking until the sauce thickens, about 5-7 minutes. Stir in garlic powder, onion powder, nutmeg (if using), remaining 1/2 tsp salt, and 1/4 tsp black pepper.

Remove the skillet from heat. Add cheddar cheese and 3/4 cup of the Gruyere cheese (reserving 1/4 cup for topping). Stir until the cheese is completely melted and the sauce is smooth and creamy.

Add the cooked pasta, broccoli, and chicken to the cheese sauce in the skillet. Stir gently until everything is evenly coated.

Pour the mixture into the prepared 9x13 inch baking dish, spreading evenly. In a small bowl, combine panko breadcrumbs and melted butter. Sprinkle the breadcrumb mixture and the remaining 1/4 cup reserved Gruyere cheese over the top of the pasta bake.

Bake for 20-25 minutes, or until the topping is golden brown and the sauce is bubbly.

Let stand for 5-10 minutes before serving to allow the sauce to set slightly. Serve hot.