In a large skillet, heat 2 tablespoons of extra virgin olive oil over medium heat. Add the ground chicken and cook until it is browned and fully cooked, about 5-7 minutes. Break it up using a spatula as it cooks.
Add the finely diced yellow onion and red bell pepper to the skillet and sauté for about 3-4 minutes until they are soft. Stir in the minced garlic, chili powder, smoked paprika, cumin, kosher salt, and black pepper. Cook for an additional minute until the spices are fragrant.
To the skillet, add the drained black beans, chopped green chilies, chopped spinach, frozen corn, cilantro, lime juice, and lime zest. Stir everything together and cook for another 2-3 minutes, just until the spinach wilts. Remove from heat and let it cool slightly.
Preheat your oven to 400°F (200°C). Lay out the flour tortillas on a clean surface. Spoon about 2-3 tablespoons of the filling onto the lower third of each tortilla. Sprinkle with shredded pepper jack cheese.
To roll the tortillas, fold the sides over the filling, then roll from the bottom up tightly. Place the rolled egg rolls seam-side down on a parchment-lined baking sheet. Repeat with the remaining tortillas and filling.
Using a pastry brush, lightly brush the tops of each egg roll with the remaining 2 tablespoons of extra virgin olive oil. This will help them crisp up nicely in the oven.
Bake the egg rolls in the preheated oven for 15-20 minutes, or until they are golden brown and crispy. Be sure to flip them halfway through for even browning.
Remove the egg rolls from the oven and let them cool slightly before serving. These Baked Southwestern Chicken Egg Rolls are delicious on their own or served with your favorite dipping sauce, such as salsa or guacamole.