Tie together the parsley and thyme sprigs with kitchen twine.
Heat a large, wide saucepan or deep skillet over medium-low heat.
Add the olive oil and shallots. Cook, stirring, until the shallots begin to soften, about 1 minute.
Add the garlic and cook for another minute.
Add the wine, cream, salt, and pepper, then stir well to combine.
Add the herb sprigs and bring the mixture to a boil.
Add the mussels, cover the pan, and cook until the mussels have opened, about 5 minutes.
Remove the pan from heat and discard any mussels that didn’t open. Discard the herb sprigs.
Pour the mussels and their liquid into a deep serving bowl, sprinkle with the chopped parsley, and serve immediately.