Preheat the oven to 425 degrees F.
Toss the broccoli with 1 tablespoon olive oil, salt and pepper and spread it across on a sheet pan in a single layer.
Roast the broccoli until it is crisp-tender and starting to brown at the edges, about 10-12 minutes.
For the pesto, finely chop 1 cup roasted broccoli, garlic, pine nuts, Parmesan and lemon juice in a food processor or blender.
With the motor running, pour in ½ cup olive oil through the feeder tube, processing the mixture until it is fully combined.
Cook the pasta until al dente according to package instructions. Reserve ½ cup pasta cooking water before draining.
In a large bowl, stir the pesto into the pasta. Then fold in the remaining roasted broccoli.
Add a little cooking water as needed to help the pesto coat the noodles. You may not need the entire ½ cup.
Divide into serving bowls or onto plates and top with additional parmesan as desired.
