Preheat the oven to 425°F (218°C). Line a rimmed baking sheet with parchment paper and set aside.
Heat 2 tablespoons olive oil in a 12-inch skillet over medium heat.
Add the ground chicken, diced yellow onion, and diced red bell pepper to the skillet; season with chili powder, smoked paprika, cumin, kosher salt, and black pepper. Cook over medium heat, breaking up the chicken, until the meat is browned and the vegetables are softened, about 6–8 minutes.
Stir in the minced garlic and cook for 1 minute more.
Reduce heat to low. Add the drained black beans, chopped green chilies, chopped spinach, frozen corn, chopped cilantro, lime juice, and lime zest. Stir to combine.
Gently simmer on low until the spinach is wilted and most moisture has evaporated, about 8–10 minutes. Remove from heat and stir in the shredded pepper jack cheese until evenly melted and distributed.
Lay a tortilla flat and place an equal portion of the filling down the center, leaving about 1 inch clear on each end. Fold the short ends in, then roll tightly to enclose the filling. Repeat with remaining tortillas and filling.
Place each rolled tortilla seam-side down on the prepared baking sheet. Brush the tops with the remaining 2 tablespoons olive oil.
Bake for about 15 minutes or until golden brown and crisp on top. Remove from oven and serve warm.
