Heat the oven and prep the peppers. Preheat the oven to 375°F. Lightly oil a 9x13-inch baking dish. Halve the bell peppers lengthwise through the stem and scoop out the seeds and white membranes with a spoon. A grapefruit spoon works brilliantly for this if you have one. Arrange the pepper halves cut-side up in the baking dish so they fit snugly — they should support each other and not tip over.
Par-bake the peppers. Brush or drizzle the peppers lightly with olive oil and sprinkle with a pinch of salt. Bake for 12 to 15 minutes while you make the filling. This head start softens them just enough so they finish tender at the same time as the filling heats through. Do not skip this — raw peppers stuffed and baked straight will still be crunchy when everything else is done. Pour off any liquid that collects in the dish.
Cook the filling base. While the peppers par-bake, heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the diced onion and cook 4 to 5 minutes until soft and translucent. Stir in the garlic, cumin, chili powder, smoked paprika, and oregano; cook 1 minute until fragrant. Your kitchen should smell incredible right about now.
Combine the filling. Add the black beans, corn, and drained diced tomatoes to the skillet. Stir and cook 2 to 3 minutes until everything is heated through. Remove from the heat and fold in the cooked rice, salt, black pepper, 1 cup of the shredded cheese, and the cilantro. Taste and adjust the seasoning — the filling should taste bold and well-salted on its own, because the mild peppers will mellow it out.
Stuff the peppers. Spoon the filling generously into each par-baked pepper half, mounding it slightly on top. Pack it in with the back of the spoon so there are no air pockets. Sprinkle the remaining 1/2 cup of cheese evenly over the tops.
Bake. Cover the dish loosely with foil and bake for 20 minutes. Remove the foil and bake 10 to 15 minutes more, until the peppers are tender when pierced with a knife and the cheese is melted with golden-brown spots. If you like extra browning, switch on the broiler for the last 1 to 2 minutes — but watch it like a hawk, because cheese goes from golden to burnt fast.
Rest and serve. Let the peppers rest for 5 minutes out of the oven; the filling sets up slightly and they are easier to serve. Top with extra cilantro and serve with sour cream, salsa, and lime wedges on the side. I set out the toppings buffet-style and let everyone build their own plate.