Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces and cook until browned on all sides, about 5 minutes. Remove chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook until softened, about 3 minutes.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the rinsed rice to the skillet and stir to coat with the oil, onion, and garlic mixture. Cook for 1-2 minutes to lightly toast the rice.
Pour in the chicken broth and milk, then stir in the diced tomatoes with green chilies, ground cumin, chili powder, smoked paprika, salt, and black pepper.
Return the browned chicken pieces to the skillet and stir to combine.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 18-20 minutes, or until the rice is tender and the liquid is absorbed.
Remove the skillet from heat and immediately stir in the shredded cheddar and Monterey Jack cheeses until melted and creamy.
If using, stir in the finely chopped jalapeño pepper for a bit of heat.
Garnish with chopped fresh cilantro before serving.