Preparation Preheat oven to 350°F. Spread out hazelnuts on a small rimmed baking sheet and toast, tossing occasionally, until golden, about 6 minutes. Let cool, then coarsely chop; set aside. Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente (about 5 minutes for fresh pasta). Drain, reserving 1 cup pasta cooking liquid. Meanwhile, heat oil in a large skillet over medium-high heat. Add squash and cook, tossing occasionally, until crisp-tender, about 5 minutes. Add garlic and 1/4 teaspoon red pepper flakes and cook, stirring, just until garlic begins to brown, about 2 minutes. Immediately add 1/2 cup pasta cooking liquid to keep garlic from burning; reduce heat to low and gradually add butter, swirling skillet and adding more pasta cooking liquid as needed, until a thick, glossy sauce forms. Add pasta to skillet with squash and sauce and toss to coat. Add lemon juice, 1/4 cup Parmesan, 2 tablespoons mint, and remaining 1/4 teaspoon red pepper flakes and toss to combine; season with salt and pepper. Serve pasta topped with reserved hazelnuts, more Parmesan, and remaining 2 tablespoons mint. DO AHEAD: Hazelnuts can be toasted 5 days ahead. Store airtight at room temperature.
Preparation Preheat oven to 350°F. Spread out hazelnuts on a small rimmed baking sheet and toast, tossing occasionally, until golden, about 6 minutes. Let cool, then coarsely chop; set aside. Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente (about 5 minutes for fresh pasta). Drain, reserving 1 cup pasta cooking liquid. Meanwhile, heat oil in a large skillet over medium-high heat. Add squash and cook, tossing occasionally, until crisp-tender, about 5 minutes. Add garlic and 1/4 teaspoon red pepper flakes and cook, stirring, just until garlic begins to brown, about 2 minutes. Immediately add 1/2 cup pasta cooking liquid to keep garlic from burning; reduce heat to low and gradually add butter, swirling skillet and adding more pasta cooking liquid as needed, until a thick, glossy sauce forms. Add pasta to skillet with squash and sauce and toss to coat. Add lemon juice, 1/4 cup Parmesan, 2 tablespoons mint, and remaining 1/4 teaspoon red pepper flakes and toss to combine; season with salt and pepper. Serve pasta topped with reserved hazelnuts, more Parmesan, and remaining 2 tablespoons mint. DO AHEAD: Hazelnuts can be toasted 5 days ahead. Store airtight at room temperature.