Preheat oven to 375°F. Cut squash in half lengthwise; remove seeds. Place squash cut-side down on a parchment-lined baking sheet. Roast until soft, about 1 hour. Set aside to cool. Once cooled, remove skin and purée in a food processor until smooth.

Bring a large pot of salted water to a boil; cook pasta until almost tender yet firm to the bite, about 7 minutes; drain and rinse with cold water to stop the cooking process.

Meanwhile, make cheese sauce by melting butter in a large saucepan over medium heat. Whisk flour into butter until smooth, about 2 minutes. Add garlic and sage and cook for 30 seconds. Gradually whisk in 2 cups milk and stir until thickened. Add the rest of the milk and bring to a boil, stirring occasionally. Remove from heat and add squash purée, 1 cup of each cheese, Dijon, paprika, salt and pepper.

Place cooked pasta in a large bowl and fold in the butternut cheese sauce. Place in a 9x13-inch oiled baking dish, top with remaining cheese and bake uncovered for 20 minutes or until golden brown. Garnish with flaky sea salt and ground black pepper before serving.