Heat the oil in a large pot over medium heat. Add the onion, garlic, and 1 teaspoon each salt and pepper. Cook, stirring occasionally, until soft, 8 to 10 minutes.
Add the cumin and paprika. Cook, stirring, until fragrant, about 1 minute. Add the chicken, chipotles, and ¼ cup water. Reduce heat, cover, and simmer until the chicken is very tender, 35 to 45 minutes. Uncover and cook until the liquid has nearly evaporated, 5 to 10 minutes. Coarsely shred the chicken.
Meanwhile, heat ¼ inch of oil in a medium skillet over medium-high heat. Fry 2 tortillas at a time until browned and crisp, 1 to 2 minutes per side. Drain on a paper towel–lined baking sheet.
Top the tostadas with the chicken and Crunchy Slaw. Serve with the lime wedges.
