Bring to a rolling boil in a large pot 6 quarts water and salt.
Add and cook until tender but firm fresh (or dried) pasta.
Meanwhile, combine in large bowl chicken breast halves, broccoli pieces, grated lemon zest, ground red pepper, ground black pepper and pinch of salt.
Heat in large skillet over high heat olive oil. Add chicken mixture and cook, stirring, until browned, about 5 minutes. Stir in dry white wine, tomato puree, olives and capers. Simmer, uncovered, 5 minutes.
Drain pasta and toss with sauce. Serve with grated pecorino cheese.