Cook the pasta according to the package directions. Drain and return it to the pot.
Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the sausage and cook, breaking it up with a spoon, until browned, 5 to 6 minutes. Transfer to a bowl.
Wipe out the skillet and heat the remaining oil over medium heat.
Add the cabbage, shallots, ½ teaspoon salt, and ¼ teaspoon pepper and cook, stirring occasionally, until beginning to soften, 5 to 6 minutes.
Add the chicken broth and simmer until the cabbage is tender, 3 to 4 minutes.
Add the cabbage mixture to the pasta, along with the sausage and chives, and toss to combine.