In a small bowl, stir together sour cream, lime zest, lime juice, and hot sauce. Season with a pinch of salt. Cover and refrigerate until ready to serve.

In a medium bowl, toss chicken strips with chili powder, cumin, garlic powder, and 1/2 teaspoon salt until evenly coated.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add chicken in a single layer and cook undisturbed for 3-4 minutes until golden brown on the bottom. Flip and cook 2-3 minutes more until cooked through. Transfer to a plate.

Add remaining 1 tablespoon oil to the same skillet. Add peppers and onion with remaining 1/4 teaspoon salt. Cook over medium-high heat, stirring occasionally, for 6-8 minutes until softened and charred in spots. Return chicken to the skillet and toss everything together. Remove from heat.

Preheat oven to 350 degrees F. Split slider buns and arrange bottom halves on a baking sheet. Divide chicken and pepper mixture evenly among buns, then top each with a half-slice of pepper jack. Cap with top buns.

Bake for 8-10 minutes until cheese is melted and buns are warmed through. Serve immediately with lime crema drizzled over top and cilantro scattered over.