How to Make It
In a medium bowl, cover the salt cod with cold water and soak in the refrigerator for 24 hours or for up to 2 days. Change the water at least three times.
Drain the salt cod; transfer to a large saucepan. Add the milk, thyme, bay leaf and smashed garlic. Pour in enough water to cover the fish by 2 inches. Simmer over low heat for 20 minutes, until the fish flakes with a fork. Using a slotted spoon, transfer the fish to a plate and let cool. Flake the fish.
Add the potatoes to the saucepan and simmer until tender, 10 minutes. Using a slotted spoon, transfer the potatoes to a large bowl along with 2 tablespoons of the cooking liquid; mash to a coarse puree.
In a small skillet, heat the olive oil. Add the shallot and minced garlic and cook over moderate heat until softened, about 4 minutes. Scrape the mixture into the bowl with the potatoes. Add the salt cod, cilantro, piment d'Espelette and egg yolk and stir until blended. Refrigerate the mixture until chilled, at least 30 minutes.
In a shallow bowl, beat the eggs with 1 teaspoon of water. Put the flour and bread crumbs in shallow bowls. Line a baking sheet with wax paper. Form the salt cod mixture into 1-tablespoon-size balls. Dredge the balls in flour, dip them in the beaten eggs and coat with the bread crumbs. Arrange the croquettes on the prepared baking sheet and refrigerate until chilled, about 10 minutes.
Fill a large, deep skillet with 1/2 inch of vegetable oil and heat until shimmering. Working in 2 batches, fry the croquettes over high heat, turning once or twice, until golden all over, about 4 minutes; drain on paper towels. Transfer the croquettes to a platter and serve with lemon wedges.