Cook broccoli for 3 minutes in a large pot of boiling water with 1 teaspoon salt. Remove from water with slotted spoon. Place in large bowl and set aside.
In same water, cook pasta according to package directions, about 10 minutes. Drain well and add to broccoli.
While pasta is cooking, in small sauté pan, heat oil and cook sliced red pepper, garlic and lemon zest over medium-low heat for 3 minutes.
Off heat, add 2 teaspoons salt, red pepper flakes, pepper and lemon juice. Mix and pour this over broccoli and pasta. Toss well.
Season to taste, sprinkle with cheese (if using), and serve. For added protein, shred 1/2 of a cooked store-bought roasted chicken, then toss with pasta and serve.