Prepare the mussels: Rinse the mussels thoroughly under cold water, scrubbing the shells if necessary. Discard any mussels that are cracked or do not close when tapped.

Sauté the onions and garlic: In a large pot or Dutch oven, heat the butter and olive oil over medium heat. Add the chopped onion and garlic and sauté for 3-4 minutes until softened and fragrant.

Deglaze with white wine: Pour in the white wine (if using) and simmer for 2-3 minutes to reduce slightly. Add the broth and bring the mixture to a simmer.

Cook the mussels: Add the cleaned mussels to the pot, cover, and cook for 5-7 minutes, or until the mussels have opened. Discard any mussels that do not open.

Finish with cream: Stir in the heavy cream and fresh thyme. Simmer for another 2-3 minutes until the broth is rich and creamy. Adjust seasoning with salt and pepper to taste.

Serve: Ladle the mussels and broth into bowls. Garnish with fresh parsley and serve with lemon wedges on the side, if desired. Pair with a low-carb side like sautéed spinach or zucchini noodles.