In a large skillet, heat olive oil over medium heat. Add diced red and green bell peppers and diced red onion, sautéing until softened, about 4-5 minutes. Stir in black beans and corn, cooking for an additional 2 minutes until heated through.

Incorporate shredded cooked chicken breast into the skillet, along with chili powder, cumin, garlic powder, and salt. Mix well to combine the spices evenly. Reduce heat to low, then add shredded Monterey Jack cheese and pepper jack cheese, letting them melt for about 2-3 minutes. Fold in chopped cilantro and remove from heat to let the filling cool.

Lay an eggroll wrapper in a diamond shape on your work surface. Spoon cooled filling onto the center of the wrapper. Fold the bottom corner over the filling, then fold in the sides tightly, rolling upwards to seal. Use a small amount of water on the edges to help seal the eggrolls.

In a mixing bowl, combine mayonnaise, sour cream, buttermilk, chopped cilantro, and lime juice. Season with salt and pepper and onion powder. Whisk until smooth and creamy, then cover and refrigerate the sauce for at least 30 minutes to allow flavors to meld.

In a heavy-bottomed pot, heat vegetable oil over medium heat until it reaches 350°F. Carefully place the eggrolls in batches, frying for 3-4 minutes or until golden brown and crispy. Use a slotted spoon to transfer them to a paper towel-lined plate to drain excess oil.

Serve the hot Chili's Southwest Eggrolls alongside the chilled dipping sauce for the perfect appetizer.