Cavatappi with Broccolini, Brown Butter, and Sage

Bring a large pot of water to a boil. Fill a large bowl with water and ice and set aside.
Add 1 tablespoon kosher salt and the broccolini to the boiling water and cook until crisp-tender, 2 to 3 minutes. Using a spider or slotted spoon, transfer the Broccolini to the ice water to stop the cooking and let cool. Keep the pot of water boiling for the pasta. Drain the broccolini in a colander, cut the stalks in half crosswise, and set aside.
In a large nonstick skillet over medium heat, heat the olive oil until shimmering. Add the garlic and red pepper flakes and cook, stirring frequently, for 1 minute. Add the blanched broccolini, 1/2 teaspoon salt, and 1/4 teaspoon black pepper and sauté until tender, 3 to 5 minutes. Transfer the broccolini to a medium bowl and set aside.
Add the pasta to the boiling water and cook until al dente, about 2 minutes less than the directions on the package. Reserve 1/2 cup of the pasta water and drain the pasta in a colander.
Meanwhile, wipe out the skillet, return it to medium-low heat, and add the butter. When the butter has melted, add the sage leaves and cook until the butter turns amber brown and the sage shrivels, 4 to 6 minutes. Add 1/4 teaspoon salt and black pepper. Stir in the cooked pasta until incorporated, then fold in the broccolini and 2 to 3 tablespoons of the reserved pasta water.
Stir in the Parmesan cheese, adding more pasta water until you achieve desired creaminess. Season with salt and pepper and serve hot.