Melt the butter in a large, deep pot over medium-high heat. Add onion and garlic, stirring until soft (about 2-3 minutes).
Add parsley, thyme, and mussels to the pot. Pour wine over top, cover, and cook over high heat until the mussels open (about 4-5 minutes). Shake the pot frequently as the mussels cook to make sure that they steam evenly.
Remove mussels to individual serving bowls. Ladle wine sauce over top. Serve with pasta or crusty bread and garnish with additional fresh herbs, if desired.