Melt butter in a large skillet over medium-high heat. Saute onion, carrots, celery, peppercorns, and cloves in melted butter until onions are browned, 7 to 10 minutes.
Stir flour into the onion mixture; cook and stir until the flour is completely moistened, 1 to 2 minutes. Stream beef broth into the skillet while stirring the onion mixture; cook, stirring continually, until the broth thickens into a gravy, 5 to 10 minutes. Add water to thin the gravy as needed to keep it from becoming paste-like.
Stir 1 tablespoon parsley into the gravy; continue to cook, stirring frequently, until the parsley imparts flavor to the gravy, 5 to 10 minutes; strain through a fine-mesh strainer into a clean saucepan. Discard vegetables.
Place the saucepan over low heat. Season sauce with salt, pepper, and most of the remaining parsley. Stir red wine into the sauce.
Heat olive oil in a skillet over medium-high heat; saute mushrooms in hot oil until completely tender, about 5 minutes. Stir mushrooms into the sauce; garnish with remaining parsley after spooning over steaks.