Warm oil in a large pot over medium heat. Add garlic and shallot, sprinkle with salt, and cook, stirring often, until tender, 1 to 2 minutes. Add wine, tomatoes, honey, red pepper flakes, bay leaf, basil, and thyme. Bring to a boil, then reduce heat until mixture simmers. Season broth with salt and pepper.
Add mussels, stir, bring back to a simmer, cover pot, and cook until mussels have opened (discard any that don’t open), 7 to 10 minutes. Remove and discard thyme sprig and bay leaf. Divide mussels and broth among 4 large bowls and serve hot with crusty bread, if desired.