Combine the chili powder, salt, paprika, cumin, and cayenne pepper in a small bowl. Add the chicken thighs to a large bowl, add half of the spice mix, and toss to evenly coat.

Heat the oil in a large skillet over medium heat. Once the oil is shimmering, add the chicken thighs in one single layer (you may need to cook in two batches depending on the size of your pan). Cook until crisp on each side and each reaches an internal temperature of 165F, about 6 to 8 minutes per side. Transfer to a separate dish or plate, leaving any remaining oil in the skillet.

To the same skillet, add the rice and cook, stirring frequently, until toasted, about 1 minute. Add the corn, garlic, and the remaining spice mix and mix well. Continue cooking, stirring occasionally, to warm the corn and brown it slightly, 2 to 3 minutes.

Stir in the coconut milk and broth, turn the heat to medium-high, and bring to a simmer. Reduce the heat to low, cover, and cook until the rice is tender, 13 to 16 minutes (Note: if you have a gas stove, I recommend stirring at least once halfway through to prevent sticking, your rice may only need about 10 minutes to fully cook).

Squeeze the lime juice over the rice and mix. Return the cooked chicken on top of the rice and sprinkle with the crumbled cotija or feta (if using) and chopped cilantro. To serve, evenly divide among 4 plates.