Trim the dark-green leaves and root ends from the leeks. Split the leeks lengthwise and rinse them well under cold running water. Slice them crosswise into about 1/2-inch-thick half-moons.
In a large, heavy pot, cook the leeks, garlic, and bay leaf in the oil over medium heat, stirring often, until the leeks begin to brown, about 10 minutes. Stir in the tomatoes and their juices, tarragon, and pepper flakes and simmer to meld the flavors for 5 minutes. (This mixture can be prepared up to 3 hours ahead and left out at room temperature.)
When you’re ready to cook the mussels, return the leek mixture to a boil over high heat. Add the mussels, cover, and cook, stirring occasionally, until the mussels open, 3 to 8 minutes. Spoon the mussels, broth, and vegetables into large bowls and serve with the bread for dipping in the broth.