Heat the butter and olive oil in a large pot over medium heat. Add the shallots and garlic and cook until softened, about 4 minutes.

Add the mussels, wine, saffron, and parsley and season with salt and pepper, to taste. Give it a good stir, cover the pot, and cook until all the mussels open, about 8 to 10 minutes. Discard any mussels that have not opened. Transfer to a large bowl and serve with crusty bread.