Rinse the mussels in a colander under cold running water and scrub each shell with a stiff brush. Pull out the fibrous beard by tugging it toward the hinge. Tap any open mussel on the counter and discard those that don't close within a minute, along with cracked shells.
Heat the oven to 200 C / 400 F. Lay the bread on a 33 x 46 cm / 13 x 18 inch sheet pan, brush with 1 tbsp olive oil, and toast for 8 to 10 minutes until golden at the edges and dry through. Rub the warm slices with the cut side of the halved garlic clove.
While the bread toasts, warm 4 tbsp olive oil, the sliced garlic and the chili flakes in a 28 cm / 11-inch, 6-quart pot over medium heat for 1 minute, until the garlic turns pale gold and smells sweet. Don't let it brown.
Add the cherry tomatoes and cook for 6 to 7 minutes, pressing them with a wooden spoon, until they collapse and the juices thicken slightly. Pour in the wine and simmer for 2 minutes.
Turn the heat to high and add the mussels. Cover tightly and cook for 4 to 6 minutes, shaking the pot once or twice, until most shells gape wide. Take the pot off the heat right away and discard any mussels that stayed shut.
Stir in the parsley and taste the broth before adding salt, since mussels release their own brine. Ladle into warm wide bowls and serve with the garlic toast.