Cook the broccoli in a large pot of boiling salted water until crisp-tender, 2 to 4 minutes. Transfer to a plate to cool slightly; reserve the water for cooking the tortellini.
Pulse the broccoli, parsley, oil, pine nuts, Parmesan, ½ teaspoon salt, and ¼ teaspoon pepper in a food processor until finely chopped, 15 to 20 seconds.
Cook the tortellini according to the package directions, reserving ¾ cup of the cooking water. Drain and return the tortellini to the pot.
Add the broccoli pesto and ¼ cup of the reserved cooking water and toss to combine. (Add more cooking water as needed to loosen the sauce.)
Serve sprinkled with more Parmesan.