1.Melt butter in a skillet over medium heat; cook and stir sweet onion and red onion in melted butter until softened, about 10 minutes. Cook and stir garlic into onion mixture until fragrant, about 2 minutes. Transfer to a slow cooker.
2.Pour beef stock, brandy, soy sauce, and Worcestershire sauce into slow cooker. Season with salt and black pepper.
3.Cook soup on High for 4 to 5 hours.
4.Preheat the oven's broiler and set the oven rack about 6 inches from the heat source.
5.Ladle the soup into 3 oven-proof bowls; top with croutons and a slice of Provolone per bowl.
6.Broil in the preheated oven until cheese melts and begins to brown, about 3 minutes.