Scrub mussels under cold water and pull off any beards. Discard any that stay open when tapped.
Melt butter with olive oil in a large Dutch oven over medium heat.
Add shallot and garlic, cook 2 to 3 minutes until fragrant, don't let it brown.
Pour in the white wine, bring to a simmer, and cook 1 to 2 minutes to cook off the raw alcohol smell.
Add mussels, cover with a lid, and steam 5 to 7 minutes, shaking the pot once, until shells open wide.
Discard any mussels that stayed closed. Stir in parsley, thyme, lemon juice, and red pepper flakes.
Ladle mussels and broth into bowls. Serve right away with crusty bread for dipping.