Instructions

Bring 3 quarts water to boil in large Dutch oven. Add 1 pound fettuccine and 1 tablespoon table salt and cook, stirring often, until about 2 minutes shy of al dente. Reserve 1½ cups cooking water, then drain pasta.
Meanwhile, heat 2 tablespoons extra-virgin olive oil and 3 smashed and peeled garlic cloves in 12-inch nonstick skillet over medium-low heat until pale golden and softened, about 5 minutes. Stir in ½ teaspoon pepper flakes, then transfer garlic mixture to small bowl. Heat 1 tablespoon oil in now-empty skillet over medium-high heat until shimmering. Add 1 pound broccolini, trimmed and cut into 1½-inch pieces; 2 tablespoons water; ½ teaspoon salt; and ¼ teaspoon pepper, cover, and cook until broccolini is just tender, 4 to 6 minutes; transfer to large bowl. Heat remaining 1 tablespoon oil in again-empty skillet until shimmering. Add 1 pound chicken breasts, trimmed and sliced crosswise ¼ inch thick; ½ teaspoon salt; and remaining ¼ teaspoon pepper and cook until chicken is cooked through, 4 to 6 minutes; transfer to bowl with broccolini.
Transfer garlic mixture to blender and add 1½ cups cottage cheese, 1 cup grated Parmesan, 2 teaspoons cornstarch, remaining ¼ teaspoon salt, and 1 cup pasta water and blend until smooth, about 1 minute. Combine pasta and sauce in now-empty pot and bring to simmer over medium heat. Cook, stirring constantly, until sauce is thickened and coats pasta, about 2 minutes. Stir in chicken, broccolini, and 3 tablespoons chopped parsley and continue to cook, stirring, until heated through, about 2 minutes longer, adjusting consistency with additional pasta water as needed. Serve.