How to Make It
In a medium bowl, cover the guajillos with boiling water. Let stand until softened, about 10 minutes. Drain, reserving 3/4 cup of the soaking liquid. In a food processor, puree the guajillos with their soaking liquid until smooth.
Preheat the oven to 350°. In a large skillet, heat the oil. Add 1 1/2 cups of the onion and cook over moderate heat, stirring occasionally, until lightly golden, 4 to 5 minutes. Stir in the garlic and cook until fragrant, about 1 minute. Add the guajillo puree, cumin and cinnamon and cook for 3 minutes, stirring frequently. Add the chicken and cook, breaking up the meat with a wooden spoon, until no trace of pink remains, about 5 minutes. Stir in the tomatoes, black beans, olives, raisins, vinegar, sugar and broth. Simmer, stirring occasionally, until the picadillo is thickened, 8 to 10 minutes. Season with salt, pepper and juice squeezed from the 2 lime halves.
Place a single layer of tortilla chips on an ovenproof platter. Top with half of the picadillo, 1/4 cup of the chopped onions, half of the cheese and another layer of chips. Top with the remaining picadillo and cheese. Bake the nachos for about 10 minutes, until the cheese is melted. Top with the remaining 1/4 cup of onion and the jalapeño, radishes and cilantro. Serve with sour cream and lime wedges on the side.