Put the broth in a medium pot and boil. When it's boiling, pour the polenta in while stirring. Continue to stir until the overall texture is uniform and the water looks almost entirely absorbed (about a minute).
Stir in garlic and onion powder, then cover and turn the heat down to low. Cook, stirring occasionally, for 40-45 minutes. If it starts to dry out, add another tablespoon of broth.
Meanwhile, cook the sausage: removed from casings if necessary and break into small chunks. Brown on all sides, about 10 minutes total, and remove from heat.
Grate the cheese if it's not already. When the polenta is done, stir in the sausage and most of the cheese.