Season the chicken with cumin, chili powder, 1/2 teaspoon salt, and black pepper.

Heat a large 12-inch skillet over medium-high heat. Add 1 tablespoon oil, then add the chicken in an even layer. Cook for 4 to 5 minutes, stirring once or twice, until browned. Transfer the chicken to a plate.

Reduce the heat to medium. Add the remaining 1 tablespoon oil and the diced potatoes to the same skillet. Cook for 7 to 8 minutes, stirring occasionally, until the potatoes begin to soften and brown at the edges.

Add the onion, bell pepper, frozen corn, and remaining 1/2 teaspoon salt. Cook on the stovetop for 4 minutes, stirring often, until the vegetables soften.

Return the chicken and any juices to the skillet. Stir in the salsa verde and chicken broth, scraping up any browned bits from the bottom of the pan.

Cover the skillet, reduce the heat to medium-low, and simmer for 6 to 8 minutes, stirring once, until the potatoes are tender and the sauce lightly coats everything.

Turn off the heat. Stir in the lime juice, sprinkle with cilantro if using, and serve with a spoonful of sour cream or yogurt if desired.