How to Make It
Preheat the oven to 450°. On a rimmed baking sheet, toss the tomatoes and garlic with 1 tablespoon of the oil. Season with salt and pepper and arrange cut sides down. Bake for 20 minutes, until the tomatoes are soft.
Meanwhile, in a bowl, cover the chiles with boiling water and let stand for 20 minutes.
Drain the chiles, reserving 2 tablespoons of the soaking liquid. Stem and seed the chiles and transfer the chiles and their reserved liquid to a blender. Peel the tomatoes and garlic, add to the blender and puree. Season the chipotle sauce with salt and pepper.
In a skillet, heat 1/4 inch of oil until shimmering. Add a tortilla and fry over moderately high heat until crisp, 1 minute per side. Drain on paper towels. Repeat with the remaining tortillas. Discard the oil and wipe out the skillet.
Heat the remaining 2 tablespoons of oil in the skillet. Add the diced onion and cook over moderately high heat until softened. Add the chicken livers, season with salt and pepper and cook over moderately high heat, stirring, until browned on the outside and medium within, 4 minutes. Add the chipotle sauce and bring to a simmer. Remove from the heat.
Spread the tostadas with the refried beans. Spoon the livers and sauce on top. Garnish with sliced onion and cilantro and serve.