Add all pesto ingredients to a food processor. Blend on low for about 1 minute until blended but still slightly chunky. Adjust consistency with extra olive oil, lemon juice, or water as needed.
Cook pasta according to package directions. If using broccoli, add florets to the boiling water in the last 3 minutes.
Drain pasta and toss with the pesto while still warm.
Top with extra Parmesan and fresh arugula. Add sautéed vegetables or chicken if desired.