Place a large nonstick skillet over medium heat. When hot, add the sausage and cook, breaking up with a wooden spoon 6 to 8 minutes, until browned. Transfer to a plate.
Add the oil to the skillet, brussels sprouts, shallots and garlic and cook on medium-high until golden on the edges, 4-5 minutes. Set aside with the sausage.
Add the parsnip noodles to the skillet over medium heat with the broth and red pepper flakes and cook until the noodles are al dente, about 5 minutes.
Return the sausage and brussels to the skillet, add the cheese and stir to combine.