Kerchief Pasta with Caramelized Squash and Fresh Herbs

In a braiser over medium-high heat, melt 3 Tbs. of the butter. Add the squash in a single layer and cook, without stirring, until browned underneath, about 6 minutes. Stir the squash and cook until browned on all sides, about 4 minutes more. Add the sugar, broth, salt and pepper, cover and cook until the squash is tender, 2 to 3 minutes. Uncover and continue cooking, stirring occasionally, until the liquid evaporates and the squash is dark brown and glazed, 2 to 3 minutes more. Transfer the squash mixture to a bowl.

In the same pan over medium-high heat, melt the remaining 6 Tbs. butter until light brown spots appear, about 2 minutes. Add the shallots, nutmeg and sage and cook, stirring constantly, until the shallots begin to soften, about 1 minute. Remove the pan from the heat and stir in the lemon juice and parsley. Season with salt and pepper, then stir in the squash.

Meanwhile, bring a large pot of salted water to a boil over high heat. Add the pasta and cook, stirring occasionally, until al dente, about 3 minutes. Drain, reserving 1/2 cup of the cooking water. Add the pasta and the reserved cooking water to the squash mixture and toss to combine.

Transfer the pasta to a warmed large, shallow bowl and sprinkle with some of the cheese. Serve immediately and pass the remaining cheese alongside. Serves 4 to 6.