Remove stems and seeds from the ancho peppers; toast them in a dry pan over medium heat 1–2 minutes per side until fragrant, then place in a small bowl and cover with boiling water. Soak 15 minutes, then drain.
In a blender, combine the soaked ancho peppers, chopped jalapeño, the undrained can of whole tomatoes, chopped onion, garlic, and cilantro; blend 60–90 seconds until fairly smooth.
Pour the sauce into a large skillet or Dutch oven and stir in the chicken broth.
Add the chicken breasts to the sauce, bring to a simmer, and cook about 20 minutes, turning once halfway, until chicken is cooked through.
Reduce heat to low, remove the chicken, shred or cut into bite-size pieces, then return the chicken to the skillet and keep warm while you make the chips.
Heat the vegetable oil in a heavy pot or Dutch oven to about 350°F (175°C). In batches, fry the tortilla wedges about 1 minute total, flipping halfway, until crisp. Drain on paper towels and sprinkle with salt.
Turn off the heat under the sauce and add the fried tortilla chips, pressing them into the sauce so they soak up flavor.
Sprinkle the queso fresco (or feta) over the top and finish with chopped red onion, avocado, sliced radishes, sour cream, lime, and cilantro as desired; serve immediately.
