Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
To clean the mussels, put them in a large bowl with 2 quarts of water and the flour and soak for 30 minutes, or until the mussels disgorge any sand. Drain the mussels, then remove the "beard" from each with your fingers. If they're dirty, scrub the mussels with a brush under running water. Discard any mussels whose shells aren't tightly shut.
In a large non-aluminum stockpot, heat the butter and olive oil over medium heat. Add the shallots and cook for 5 minutes; then add the garlic and cook for 3 more minutes, or until the shallots are translucent. Add the tomatoes, saffron, parsley, thyme, wine, salt, and pepper. Bring to a boil.
Add the mussels, stir well, then cover the pot, and cook over medium heat for 8 to 10 minutes, until all the mussels are opened (discard any that do not open). With the lid on, shake the pot once or twice to be sure the mussels don't burn on the bottom. Pour the mussels and the sauce into a large bowl and serve hot.