If poaching the chicken, place the chicken in a pot with the poaching ingredients. Add enough cold water to cover the chicken and bring to a low, rolling boil. Season the water with salt; reduce the heat and poach for 45-60 minutes, turning once. Let cool in the poaching liquid to room temperature. Remove the chicken from the skin and bones and dice or pull into bite-size pieces. Strain the stock.
Heat a large Dutch oven or soup pot over medium-high heat with the canola oil, two turns of the pan. Add the onions, jalapeño peppers, garlic, thyme, spices, salt and pepper and stir for 7-8 minutes to soften and toast the spices. Add the tomatoes, hominy, corn, chicken, 6-8 cups stock (depending on how thick you like your soup) and honey and simmer for flavors to combine at a low rolling boil, 20 minutes.
Pre-heat the oven to 400°F. Spray the tortilla strips and sprinkle with salt; bake to deep golden and crispy.
Finish the soup with sherry vinegar or lime juice. Serve in shallow bowls and top with toppings of choice and crispy tortillas for mixing in.