Prepare the brown rice according to the package directions (3/4 cup dry rice — about 2 cups cooked). When the rice is about halfway through its cooking time, preheat the oven to 375°F and begin preparing the peppers and filling.
Bring a large pot of water to a boil. While the water heats, cut each bell pepper in half lengthwise, remove and discard the seeds and membranes.
Fully immerse the pepper halves in the boiling water and cook 4–5 minutes, until just tender. Drain the peppers well and arrange them cut-side up in one or two rimmed baking dishes large enough to hold all halves. Set the dishes aside.
In a large, deep skillet, heat 1 Tbsp canola oil over medium-high heat. Add the chopped yellow onion (about 1 1/2 cups) and sauté until golden, about 5 minutes.
Add the minced garlic and cook 30 seconds more. Transfer the onion–garlic mixture to a plate and set aside.
Add the remaining 1 Tbsp canola oil to the same skillet and return to medium-high heat. Add the diced chicken (1 lb). Sprinkle the chicken with 1/2 tsp chili powder, 1/2 tsp ground cumin, 1/4 tsp paprika, and season with salt and freshly ground black pepper to taste.
Cook the chicken, stirring occasionally, until no longer pink and cooked through, about 5 minutes.
Reduce the heat to medium-low. Add the can of tomatoes with green chiles (10 oz), the reserved onion–garlic mixture, the drained and rinsed black beans (1 cup), the frozen corn (1 cup), the cooked brown rice (about 2 cups), the remaining 1/2 tsp chili powder, the remaining 1/2 tsp ground cumin, 3 Tbsp chopped fresh cilantro, and 1 Tbsp fresh lime juice. Stir to combine and season with salt and pepper to taste. Cook just until the mixture is heated through, 1–2 minutes.
Spoon a heaping 1/2 cup of the filling into each pepper half, pressing gently so the filling fits evenly in the cavity.
Pour enough water into the bottoms of the baking dish(es) to reach about 1/8 inch in depth, being careful not to pour water into the peppers themselves.
Cover the baking dish(es) tightly with foil and bake in the preheated 375°F oven for 30–35 minutes, until the peppers are soft.
Remove the foil, evenly sprinkle the tops of the stuffed peppers with the shredded Monterey Jack cheese (2/3 cup), and return the dish(es) to the oven until the cheese is melted, about 3 minutes.
Remove from the oven and serve warm. Garnish with additional fresh cilantro, and offer sour cream and Mexican-style hot sauce (optional) at the table.