In a non-reactive bowl, whisk together the minced chipotle peppers, olive oil, garlic, oregano, and cumin. Add the chicken thighs, coating thoroughly, and marinate for at least 30 minutes.
Combine rice and water in a medium saucepan. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes. Remove from heat and let sit for 5 minutes. Fluff with a fork and fold in the chopped cilantro, 1 tablespoon of lime juice, and salt to taste.
Preheat a grill pan or cast-iron skillet over medium-high heat. Grill the marinated chicken for 6-8 minutes per side or until the internal temperature reaches 165 degrees Fahrenheit. Rest for 5 minutes before dicing into 0.5-inch cubes.
Prepare the corn salsa by mixing the charred corn, red onion, jalapeño, and 1 tablespoon of lime juice in a small bowl. Season with salt.
Construct the queso sauce by combining the white American cheese, Monterey Jack, heavy cream, and green chiles in a small saucepan over low heat. Stir constantly until smooth and emulsified.
Assemble the bowls by layering the cilantro-lime rice at the base, followed by black beans and the diced chicken.
Top with the roasted corn salsa, shredded lettuce, a generous drizzle of the three-cheese queso, and a dollop of sour cream.