Build the base: In a large pot or deep skillet, melt the butter over medium heat. Add the sliced garlic and minced shallots, cooking until fragrant and the shallots are translucent, about 2-3 minutes.

Create the sauce: Pour in the white wine and bring to a boil, then reduce to a simmer. Add the blue cheese, cream, thyme, a pinch of salt, mixing until the cheese melts and the sauce becomes smooth. Let simmer for 3-5 minutes to allow the flavors to meld and the sauce to thicken slightly. Taste the sauce and add more salt if needed.

Steam the mussels: Add the cleaned mussels to the pot. Cover and cook for 5-8 minutes, mixing occasionally, until the mussels have opened. Discard any mussels that haven't opened.

Finish and serve: Remove from heat and stir in the chopped parsley. Serve immediately with plenty of crusty bread for dipping in that amazing sauce.