Cook pasta in a large pot of boiling salted water according to package label directions, adding broccoli for last 3 minutes of cooking. Drain well in a colander.
In a medium nonstick skillet warm 1 Tbsp. olive oil over medium-high heat. Add sausage and cook, turning frequently, for 10 to 12 minutes, or until well browned and cooked through. Transfer sausage to a cutting board. When cool enough to handle, cut sausage crosswise into 1/2-inch-thick slices.
Return pasta and broccoli to cooking pot and add sausage, roasted peppers, remaining olive oil, parsley, salt and pepper flakes. Toss to combine well; serve hot.