In large soup pot, cover chicken and poaching ingredients with about 2 1/2 to 3 quarts water. Bring to a boil then reduce heat to low. Simmer and poach 1 hour. Remove chicken breasts to a plate to cool. Peel and remove bones from chicken and slice the breast meat. Strain the poaching liquid and reserve.
Preheat broiler. Place poblano and red bell peppers on a baking sheet and char evenly to blacken skins all over leave oven door slightly ajar to allow the steam to escape. Place peppers in a large bowl and cover with plastic wrap to steam peppers and loosen flesh from skin.
In a small pot, cover potatoes with water and bring to a boil. Salt water and cook potatoes until very soft. Drain and mash until very smooth with some of the reserved stock.
Peel and seed peppers. Dice red bell pepper and coarsely chop poblanos. Add to a food processor, pure with a little stock until smooth. Stir into potatoes until very smooth and well-combined.
In the poaching pot, heat EVOO. Add corn, garlic, fresno or jalepeo for extra heat, coriander and cumin, and stir a few minutes over medium-high heat. Add potatoes and thin soup to desired consistency with reserved poaching liquid. Add chicken and cook to warm the meat through.
Serve soup in bowls with wedges of lime to squeeze over top, hot sauce and tortillas alongside.