How to Make It
Preheat the oven to 350°. Peel the butternut squash and cut into 1/2-inch squares, discarding the seeds and fibrous parts of the squash. Place the 1/2-inch pieces on a baking tray and season with salt and pepper. Lightly drizzle the olive oil over the top. Cover with foil and bake for 20 minutes until cooked through. Remove from the oven and set aside.
Cook the pasta in a large pot of boiling salted water, stirring once or twice until al dente, about 7-8 minutes. Drain and reserve 3/4 cup of pasta cooking liquid.
Meanwhile, heat the olive oil in a large skillet over medium-low heat. Add the shallots, season with kosher salt, and a 1/4 teaspoon of red pepper flakes. Cook until the shallots are translucent. Add 1/8 of a teaspoon of cinnamon to the pan, and stir for 1 to 2 minutes until shallots are evenly coated. Add the pasta water to the pan over low heat while gradually swirling in the butter. A glossy sauce will form in the pan.
Add the pasta and squash to the pan over medium heat, and toss to coat with the sauce. Add the lemon juice and a 1/4 cup of the Parmesan, stir to combine. Season the pasta with a generous amount of kosher salt and pepper. Sprinkle the pasta with the remaining Parmesan, cinnamon and the chopped mint leaves. Serve immediately.