Preheat the oven to 400°F. Prepare the peppers for stuffing by removing the stems then slicing the peppers in half lengthwise. Remove any seeds and membranes. Set aside.
Into a large skillet over medium-high heat, add the olive oil. When the oil is hot, add the onion and crumble the chorizo sausage into the pan. Cook for 5 minutes, stirring frequently until sausage is browned and onion is softened. Remove from heat.
Add the cheddar cheese and stir to distribute throughout.
Spoon generous portions of the sausage and cheese mixture into each pepper. Arrange the filled peppers onto a roasting pan. Bake for 15 minutes and serve hot.