Whisk together 1tbsp olive oil, lime juice, lime zest, and 2tsp Goya seasoning in a small bowl. (Do not throw away the rest of the lime.)
Transfer the mixture to a quart-sized Ziploc bag. Add the chicken. Close the bag, and toss to coat with marinade.
Get as much air as possible out of the bag.
Let marinate in refrigerator for about an hour, up to overnight.
Once the chicken has marinated, transfer it to a baking dish and cook fully. Pull or shred it and set aside.
Cut tortillas into quarters, then cut into strips.
Toss with olive oil and sprinkle with kosher salt and paprika and toss again.
Spread on a baking sheet lined with a silicone baking mat or parchment paper and bake at 350°. Check periodically to make sure none of them are burning, especially if you have hot spots in your oven.
Stir them with tongs a few times throughout the baking process.
Remove from the oven when they’re crunchy and golden.
Roast the poblanos on a baking sheet under the broiler until they’re slightly charred.
When the poblanos are cool enough to handle, preheat a dutch oven or other really large pot over medium heat. Peel off the and discard the poblano skins. Discard the seeds and membranes. Roughly chop, and set aside.
Coat the bottom of the dutch oven in a small amount of olive oil.
Add the onions, garlic, and poblanos. Cook, stirring frequently, until the onions are soft.
Add the chicken stock. Bring to a boil, then reduce to a simmer. Simmer for a few minutes. Puree everything with an immersion blender.
Add the tomatoes and black beans (including liquid from can) and stir to combine.
Add the pulled chicken, salt, and cumin. Bring to a boil, then reduce to a simmer.
Simmer covered for about 20 minutes.
Add the corn, followed by the heavy cream. Stir constantly while adding the heavy cream. Stir in the cheese.
Ladle the soup into bowls. Top with sour cream, more cheese, and tortilla strips.
If you have a KitchenAid stand mixer, cut each piece in half and add to the mixing bowl. Use the flat beater and beat for about 30-45 seconds, and it’ll pull it for you. Cover the mixer with a towel to pieces don’t fly everywhere.