Boil the pasta: Bring a large pot of salted water to a boil and cook the pasta according to the package directions until just tender.

Add the broccoli: Drop the broccoli florets into the same pot for the last 3 minutes of cooking so they turn bright green and tender-crisp.

Reserve pasta water: Scoop out 1 cup of the starchy cooking water before draining, then drain the pasta and broccoli together.

Bloom the garlic: Warm the olive oil in a large skillet over medium heat and cook the garlic and red pepper flakes for about 30 seconds, until fragrant but not browned.

Crisp the chickpeas: Add the chickpeas in a single layer and cook for 4 to 5 minutes, letting them sit undisturbed so a few edges turn golden and slightly crisp.

Mash some chickpeas: Press the back of a spoon into about a quarter of the chickpeas right in the skillet to release their starch and thicken the base.

Combine everything: Add the drained pasta and broccoli to the skillet along with the reserved pasta water, parmesan, lemon zest and lemon juice.

Toss into a sauce: Toss over low heat for 1 to 2 minutes until the parmesan melts into a light sauce that coats the pasta evenly.

Season and serve: Taste and season with salt and black pepper, then divide among bowls while still warm.