
Bring chicken, onion, carrot, garlic, chipotles, jalapeño, and 16 cups water to a boil in a large soup pot; skim foam from surface.
Reduce heat to medium and simmer, continue to skim the surface throughout, until chicken is cooked through, about 45 minutes.
Transfer chicken to a plate.
Shred chicken meat and set aside.
Strain broth into another large pot. Discard remaining solids.
Set pot with strained broth over medium heat, and add cilantro sprigs. Bring broth to a simmer; cook until reduced to 8 cups, about 45 minutes.
Discard cilantro sprigs. Stir in 3 tablespoons lime juice. Season with salt and pepper.
Add chicken to broth.
Pour oil into skillet to a depth of 1″. Heat over medium heat.
Work in small batches to fry tortilla strips, turning occasionally, until crisp and golden brown.
Using a slotted spoon to transfer to paper towels to drain. Season with salt.
Cook thawed corn kernels in a large skillet over high heat until charred in spots.
Rewarm broth with chicken. Divide soup among bowls. Top generously with corn, tortilla strips, cilantro, tomatoes, avocado, queso fresco, and an additional lime wedge.