Bring a large pot of well-salted water to a boil.
Crisp the pancetta: Heat 1 tablespoon of the olive oil in a large sauté pan over medium-high heat.
Add the pancetta and cook, stirring occasionally, until crisp.
Remove the pancetta from the pan with a slotted spoon (but do not clean the pan) and reserve the pancetta.
Add the other tablespoon of oil to the pan and heat it over medium heat.
Add the shallots and cook, stirring occasionally, until tender.
Add the chickpeas and the greens, season lightly with salt, and cook until the greens have wilted, about 3 minutes.
Meanwhile, cook the cavatelli in the boiling water until just shy of al dente.
Reserve about 1 cup of the pasta cooking water and then drain the pasta.
Add the pasta, pancetta, and 1/2 cup of the pasta water to the pan with the chickpeas and greens.
Cook, adding additional pasta water if the pasta looks dry, until the pasta is al dente.
Add the Parmigiano and toss again.
Serve immediately with additional cheese, if you like.
Salty pancetta and bitter greens get tamed by the addition of earthy chickpeas in this hearty pasta dish.
I like to use dandelion greens in this dish.