Place rice in a colander or a fine mesh strainer and rinse under cold running water until the water runs clear. Combine rice, water, and 3/4 teaspoon of the salt in a medium saucepan and bring to a boil over high heat. Cover the pan and reduce heat to low; cook until water has been completely absorbed, about 10 minutes (rice will be slightly undercooked). Remove the lid and set the pan aside to let rice cool.
Place beans in a large mixing bowl. Using a potato masher or the back of a fork, lightly mash them (some whole beans will remain). Stir cumin, sour cream, Cotija, cilantro, tomatoes, scallions, jalapeño, pepper, and remaining salt into mashed beans and mix until evenly combined. Gently mix in cooled rice. Taste mixture and, if necessary, season with salt and freshly ground black pepper. (Note that the filling should be quite salty to compensate for there being no salt on the peppers.) Stuff each pepper with the filling and replace caps, securing with a toothpick.
Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and spread coals out evenly over the charcoal grate. Place stuffed peppers on their sides and close the lid. Roll each pepper a quarter turn every 7 minutes or so to cook all four sides. The peppers are finished once the filling is hot, the skins are well-charred, and the flesh is soft to the touch, about 30 minutes. Remove from the grill and serve.