MELT butter in large heavy skillet over medium-high heat. Add sausage and cook until edges are crisp, about 5 minutes. Stir in garlic and cook for another minute.
ADD milk, broth, beans and thyme to skillet. Season with salt and pepper, to taste. Bring mixture to simmer, reduce heat to low and continue to cook, stirring occasionally, until thickened, about 15 minutes.
SPOON bean and sausage mixture over toasted bread of choice and top with parsley and Parmesan cheese.