Gather the ingredients.
Heat olive oil in a large, deep skillet over medium heat. Add onion with a pinch of salt; cook and stir until onion has softened and turned translucent, about 5 minutes. Stir in sausage and cook until browned, 5 to 7 minutes.
Pour 1 ½ cups chicken broth into sausage mixture and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon.
Add orecchiette pasta; cook and stir pasta in hot broth, adding remaining broth when liquid is absorbed, until pasta is cooked through and most of the broth is absorbed, about 15 minutes.
Stir arugula into sausage-pasta mixture until arugula wilts.
Ladle pasta into bowls and sprinkle with Parmigiano-Reggiano cheese.