Preheat the oven to 375 degrees F.
Slice the peppers in half (cutting from the stem to the base). Using a spoon, scrape out and discard the core and seeds. Arrange the peppers in a glass baking dish or on a baking sheet so that the hollow side is facing upwards. (They can be arranged close enough to be touching.)
Set ¼ cup of the grated cheddar cheese aside. In a large mixing bowl, combine the remaining 1 cup cheese and all of the remaining ingredients, stirring to distribute evenly. Fill the peppers with the rice mixture, packing it gently to compress it inside the peppers. Bake the peppers until the rice starts to turn golden and crisp on the top and the peppers soften, 15-20 minutes. Sprinkle the remaining ¼ cup of cheese over the peppers and continue baking until the cheese melts, about 2 minutes more.
Serve immediately, topped with sour cream (if desired).