Heat 1 tablespoon olive oil in a large high-sided oven-safe skillet or cast-iron skillet over medium heat until shimmering (if using cast iron, coat the sides and bottom of the skillet with cooking spray first). Add 1 cup long-grain white rice and cook, stirring occasionally, until lightly toasted and fragrant, 3 to 4 minutes.
Reduce the heat to low. Stir in 1 thinly sliced medium yellow onion, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Cook, stirring occasionally, until the onions are just starting to soften, about 3 minutes.
Stir in 3 minced garlic cloves and cook until fragrant, about 30 seconds. Stir in 2 cups low-sodium chicken broth, 1 (16-ounce) jar salsa verde, 2 cups shredded, cooked chicken, 1 cup frozen corn kernels if using, and 1 chicken bouillon cube.
Remove the skillet from the heat. Sprinkle 1/2 cup of the shredded Monterey Jack cheese over the chicken and rice mixture. Transfer the skillet to the oven and bake for 25 minutes.
Remove the skillet from the oven and give the mixture a stir. Arrange 5 to 6 (about 6-inch) corn tortillas evenly over the top until it’s mostly covered (they can overlap, and you can tear each one into 4 pieces first if you’d like). Sprinkle with the remaining 1/2 cup shredded Monterey Jack cheese.
Return the skillet to the oven and bake until the cheese on top is melted and browned in spots, 20 to 25 minutes more. Let cool for 5 minutes before serving with desired toppings.