In a small skillet, heat 1 tablespoon oil over medium heat. Add the onion and garlic and cook until the onion is soft and the garlic is just beginning to brown, about 5 minutes. Stir in the allspice and cook, stirring, for 2 minutes. Stir in the tomatoes with some of their juice, 1/2 cup chicken broth, the chile and adobo sauce, espresso powder, peanut butter cups, raisins and 1/4 teaspoon salt. Simmer over low heat for about 5 minutes, stirring occasionally. Let cool slightly.
Meanwhile, in another large skillet, heat the remaining 1 tablespoon oil over medium-high heat. Season the chicken cutlets with salt and pepper, then cook for 3 minutes per side. Remove from the skillet and cover loosely with foil to keep warm.
Using a food processor, puree the cooled sauce with the remaining 1/4 cup chicken broth, scraping down the sides if necessary. Spoon the mole sauce over the chicken.