Remove seeds and membranes from chile peppers. Stuff each pepper with a strip of Cheddar.
Mix milk, 1 cup flour, egg, baking powder, baking soda, salt, and 1 teaspoon canola oil together in a small bowl until well combined. Place remaining ½ cup flour on a shallow plate.
Pour 1 inch oil into a heavy frying pan. Heat over medium-high heat.
Roll each pepper in flour, then dip in batter. Fry in batches until lightly browned on both sides.
