Bring a large pot of salted water to a boil. Once boiling, add broccoli and kale and cook for 2 minutes, until soft but broccoli is still bright green. Using a slotted spoon, remove vegetables to a large bowl of ice water to stop the cooking.
Meanwhile, drop pasta in the boiling water and set a timer as indicated in package directions.
Drain the broccoli and kale from the ice water and pat dry with a paper towel. Add to the bowl of a food processor along with olive oil, Parmesan, lemon juice, garlic, salt and pepper. Pulse until smooth.
Drain the pasta, reserving 1/2 cup pasta water. Transfer pasta to a large bowl, add half the pesto and stir to combine. Loosen the pesto with 1/4 cup pasta water if necessary. Serve immediately.
TIP: Freeze the remaining pesto in a tightly covered container.