Preheat the broiler. Brush the bread with olive oil and transfer to a baking sheet. Broil the bread a few inches from the heat, turning once, for 2 minutes, until golden and toasted. Lightly rub the whole garlic clove over the toasts.
Add the mussels and cook, stirring, for 1 minute. Add the wine, cover, and steam the mussels until they open, about 5 minutes. Remove from the heat.
Using a slotted spoon, transfer the mussels to four deep bowls, discarding any mussels that do not open.
Add the butter and parsley to the broth, swirling and shaking the pot until the butter melts.
Slowly pour the broth over the mussels, stopping before you reach the grit at the bottom of the pot.
Serve the mussels with the garlic toasts.
