Bring a medium pot of water to boil and place a bowl of ice water nearby. Blanch the broccoli in the boiling water for 30 seconds, and then use a slotted spoon to scoop it into the ice water to stop the cooking process. Drain and pat dry.

Place the broccoli into a food processor with the basil, olive oil, cheese, lemon juice and zest, garlic, salt, and several grinds of fresh pepper. Pulse until combined.

If desired, toss the pesto with the cooked pasta. Serve with pine nuts, red pepper flakes, and additional cheese. Season to taste and serve.