Lightly sweat the garlic, leeks and onion with the oil in a large pot over medium-high heat.
Add the mussels to the pot and toss them with the vegetables, allowing the mussels to absorb the flavor of the garlic, leeks and onion.
Deglaze the pot with the wine. Add the butter, thyme and salt and pepper to taste. Cook until the wine cooks off and the mussels open, about 3 minutes.
Serve immediately with crusty bread.