Heat the olive oil in a large, deep skillet.
Add the onion and cook, stirring often, until softened and translucent, about 3 to 4 minutes.
Stir in the garlic.
Add the ground turkey, salt, pepper, chili powder, cumin, and smoked paprika. Cook, breaking up the meat, until no longer pink, about 5 to 7 minutes.
Stir in the salsa, green chiles, black beans, and corn. Cook for 1 to 2 minutes, until warmed through.
Stir in the cooked rice and mix well.
Top evenly with Monterey Jack and cheddar.
Let the cheese melt in the skillet, or broil an oven-proof skillet for 1 to 2 minutes, watching closely, until melted and lightly browned.
Garnish with minced fresh cilantro, if desired.