In a large skillet, over medium heat, sauté the garlic in the olive oil until golden.
Bring a large pot of salted water to a boil.
Add the chicken broth carefully to the garlic so that it doesn’t splatter ([when it’s combined with the oil)]. When the broth is hot, add the broccoli, cover, and cook until tender, 5 – 10 minutes, but not soft (so that the broccoli retains its bright green color and does not become mushy or fall apart). Add about 1 teaspoon each of salt, black pepper and/or crushed red pepper, depending on your taste.
Cook the cavatelli until al dente (about 1 minute less than the package directions) and drain. Add to the broccoli and toss to combine.
Serve immediately with grated Parmigiano.
You can also make this into more of a soupy dish by adding extra broth. It is best eaten with a spoon, regardless of how much broth you add.