Step 1
Position racks in upper and lower thirds of oven; preheat to 450 degrees F.

Step 2
Place squash cut-side down in a microwave-safe dish; add 2 tablespoons water. Microwave, uncovered, on High until the flesh is tender, about 10 minutes. (Alternatively, place squash halves cut-side down on a rimmed baking sheet. Bake in a 400 degrees F oven until the squash is tender, 40 to 50 minutes.)

Step 3
Meanwhile, heat oil in a large skillet over medium heat. Add broccolini, garlic and red pepper (if using); cook, stirring frequently, for 2 minutes. Add water and cook, stirring, until the broccolini is tender, 3 to 5 minutes more. Transfer to a large bowl.

Step 4
Use a fork to scrape the squash from the shells into the bowl. Place the shells in a broiler-safe baking pan or on a baking sheet. Stir 3/4 cup mozzarella, 2 tablespoons Parmesan, Italian seasoning, salt and pepper into the squash mixture. Divide it between the shells; top with the remaining 1/4 cup mozzarella and 2 tablespoons Parmesan

Step 5
Bake on the lower rack for 10 minutes. Move to the upper rack, turn the broiler to high and broil, watching carefully, until the cheese starts to brown, about 2 minutes.