In a Dutch oven cook pasta according to package directions, adding the Broccolini for the last 4 minutes of cooking time. Drain; rinse with cold water and drain again. Set aside.
In a 12-inch skillet, heat oil over medium-high heat. Add chicken sausage, onion, and garlic. Cook, turning occasionally, until sausage is browned, about 3 minutes. Add pasta mixture, chicken broth, salt and pepper. Heat through. Add arugula and dill. Remove from heat; toss to wilt greens.
Divide among shallow bowls. Sprinkle each serving with Parmesan cheese. Drizzle with a little olive oil and sprinkle with crushed red pepper, if desired.