This is a Puglian dish, not one from anywhere near here, and we make no pretense otherwise -- some recipes belong to a place clearly enough that trying to claim them as your own family's tradition would just be dishonest. We simply liked it enough to put it on the menu.
Serves 4.
Bring a large pot of well-salted water to a boil. Add the cime di rapa and cook for about three minutes, then add the orecchiette directly to the same pot and cook everything together until the pasta is just short of al dente -- there is no need for two pots here, and the greens flavor the water the pasta cooks in.
Meanwhile, warm a generous amount of olive oil in a wide skillet, and add the garlic, anchovies, and chili. Cook gently until the anchovies dissolve into the oil and the garlic turns pale gold.
Scoop out some pasta water, then drain the orecchiette and greens together, and add them to the skillet. Toss well, breaking the greens up a little as you go, and loosen with pasta water until everything is glossy and well coated.
If the greens taste unpleasantly bitter rather than pleasantly assertive, they weren't cooked long enough, or the stems weren't trimmed of their tougher, more bitter parts before going into the pot. If the finished dish feels dry, it needed more olive oil or more pasta water at the tossing stage -- this is meant to be glossy, not merely damp. And if the anchovies taste sharply fishy instead of simply savory, they cooked too hot for too long; a gentle melt, not a fry, is what you're after.