Bring a pot of salted water to a boil. Once boiling, add the broccoli and cook for 2 to 3 minutes, just until it is bright green and slightly tender. Remove the broccoli from the water and place directly in an ice bath to stop the cooking. Once cold, drain all the water.
You can save this water if you want, because we have to cook the tortellini. Or dump it and fill the same pot with brand new water.
Transfer the broccoli to a food processor. Add in a big pinch of salt and pepper, the garlic, the arugula, parmesan, lemon juice and olive oil. Blend until combined and sauce-like, scraping down the sides if needed. Taste and season more with salt and pepper if needed. This pesto is now ready to go! If making it ahead, it can live in the fridge for a few days before using.
Bring another pot of salted water to a boil for the tortellini. Cook according to the directions, which is probably 3 to 5 minutes. Drain the tortellini and place it in a large bowl.
Add a few scoops of the pesto in with the tortellini, tossing it gently to combine. You want all the pieces coated and you can use as much or as little tortellini as you’d like! The pesto will cool down the pasta, and the warmth will also help spread the pesto around.
Once the tortellini is coated, add in the tomatoes and shaved parmesan.