Preheat broiler, with the rack 6 inches from the heat source. Place chiles on a baking sheet. Broil, flipping once, until charred, 10 to 15 minutes. Transfer to a heatproof bowl, and cover with plastic wrap. Let stand 15 minutes. Remove skins and seeds, and discard. Cut chiles into 1/2-inch-thick strips, and set aside.
Heat oil in a large nonstick skillet over medium heat. Add onion. Cook, stirring often, until onion is translucent and pale golden, 10 to 12 minutes. Stir in beans, stock, and salt. Using a heatproof rubber spatula, fold in chiles; cook until chiles are warmed though, 3 to 5 minutes.
Remove from heat; stir in 1 tablespoon fromage blanc. Spoon into the warm tortillas. Top with remaining 3 tablespoons fromage blanc, dividing evenly. Serve with lime, and garnish with cilantro.