Place the boneless, skinless chicken breast in a medium saucepan. Season it to taste with kosher salt and black pepper.
Pour in enough water to submerge the chicken beneath at least 1 inch of water.
Set the saucepan over medium-high heat and bring the water to a boil.
Once boiling, cover the saucepan, lower the heat, and gently simmer the chicken for 15–20 minutes, adjusting the cooking time according to its thickness. Continue cooking until the center of the chicken reaches an internal temperature of 165°F.
Remove the cooked chicken and place it in a large bowl or the bowl of a stand mixer. Shred it using two forks, or use the stand mixer to separate the meat into shreds.
In a separate large mixing bowl, combine the full-fat Greek yogurt or skyr with the freshly squeezed lime juice, ground cumin, chili powder, smoked paprika, kosher salt, and black pepper. Add cayenne pepper to taste if additional heat is desired.
Whisk the mixture thoroughly until the seasonings are evenly incorporated and the yogurt forms a smooth, creamy dressing.
Add the shredded chicken to the bowl containing the seasoned yogurt mixture.
Add the drained black beans, diced red bell pepper, corn kernels, finely chopped red onion, and chopped cilantro.
Stir until the chicken, beans, and vegetables are evenly distributed and thoroughly coated with the creamy yogurt dressing.
Taste the finished mixture and adjust the kosher salt, black pepper, or optional cayenne as needed.
Place the prepared chicken salad in the refrigerator and chill it for at least 30 minutes so the flavors have time to blend.
After chilling, serve the Southwestern chicken salad on whole-wheat toast, alongside tortilla chips, over a rice cake, or inside a tortilla as a wrap.