For the topping: Preheat the oven to 400 degrees F.
Mix together the panko, olive oil and salt in a small bowl. Set aside.
For the pasta: Heat a large ovenproof braiser over medium heat. Melt the butter in the braiser and add the shallots, pepper flakes and 1/2 teaspoon salt. Cook until the shallots begin to soften, about 2 minutes. Whisk in the flour and stir to cook out some of the raw flour taste, about 2 minutes. Slowly begin to add the milk, adding a small amount at a time and whisking after each addition, until smooth. Bring to a simmer, then reduce the heat to maintain a simmer for 5 minutes. Stir in the goat cheese, 1 cup mozzarella and the squash. Season with the remaining 1 1/2 teaspoons salt.
Meanwhile, bring a large pot of water to a boil over high heat. Season well with salt. Cook the pasta for about 6 minutes (it should still be very firm). Using a pasta spider, remove the pasta directly to the sauce but do not yet stir it in. Sprinkle the plain pasta with the Parmesan and stir to combine. Add the broccoli rabe to the pasta water and cook for 30 seconds. Use the pasta spider to drain well, then add to the pasta. Stir to evenly distribute. Sprinkle the top with the remaining 1/2 cup mozzarella and the panko mixture. Bake until bubbly all over, 20 to 25 minutes. Switch to the broiler and broil for 5 minutes to brown the top, if desired.