Spicy Penne Tossed with Chicken, Broccoli and Chopped Olives

Bring a large pot of well-salted water to a boil over high heat. Meanwhile, heat the oil and garlic in a 12-inch skillet over medium heat, stirring gently so the cloves don’t break up, until they become light brown in places and very fragrant, 2 to 3 minutes. Add the rosemary and red pepper flakes and cook until they start to sizzle, about 15 seconds. Add the chicken, sprinkle with 1/4 tsp. salt, and cook, stirring often, until the chicken loses its raw color, about 2 minutes. Remove from the heat and stir in the olives.

Add the penne to the boiling water and cook, stirring occasionally, until just barely al dente, 1 to 2 minutes less than the package instructions. Add the broccoli and cook until it turns bright green and the pasta is tender, about 1 minute. Reserve 1/2 cup of the pasta water, and then drain the pasta and broccoli. Discard the garlic from the olive mixture. Add the pasta and the pasta water to the skillet and cook uncovered over medium-high heat, stirring, until the pasta absorbs most of the liquid, about 2 minutes. Stir in the lemon juice and half of the Pecorino. Serve sprinkled with the remaining Pecorino.