Preheat oven to broil with rack in middle position. Heat 2 tablespoons oil in a large skillet over medium-high heat until shimmering. Sprinkle chicken with ½ teaspoon cumin. Add the chicken to the pan; cook, undisturbed, until golden brown on both sides and an instant-read thermometer inserted into the thickest portion registers 165°F, 4 to 5 minutes per side. Transfer the chicken to a plate. Do not wipe the skillet clean.
Add chopped onion and jalapeño to the skillet. Cook over medium-low heat, stirring often, until softened and starting to brown, 2 to 3 minutes. Add ½ cup corn, minced garlic, ¼ teaspoon salt and the remaining 1 teaspoon cumin; cook, stirring constantly, until the garlic is fragrant, about 30 seconds. Stir in rinsed beans, undrained green chiles and ½ cup broth; bring to a boil. Reduce heat to medium-low and simmer, undisturbed, until reduced by half, 3 to 4 minutes. Remove from heat. Stir in cubed cream cheese, ¼ cup sour cream, and ½ cup pepper Jack, stirring until the cream cheese is melted, about 2 minutes. Return the chicken to the pan and turn to coat.
Sprinkle the mixture with the remaining ½ cup pepper Jack. Broil until the cheese begins to brown and the chicken is warmed through, about 4 minutes. Sprinkle with ½ cup tortilla strips. Garnish with cilantro, if desired.
