Heat a skillet over medium heat and add the canola oil. When the oil is hot, cook the ham, red onion, and bell peppers until softened, 4 to 5 minutes. Remove from the pan and set aside.
In a small bowl, whisk together the eggs and salt and pepper.
Coat the skillet with cooking spray and put it over medium-low heat. Add the beaten eggs and gently stir with a spatula or wooden spoon. Cook the eggs until they set, 4 to 5 minutes. Put the cooked ham and vegetables back into the pan and stir to combine.
Wrap the tortillas in a damp towel and microwave for 30 seconds to warm them. Put a tortilla on a plate, add half the egg mixture, and top with half the cheese. Wrap the ends of the tortilla up and then fold in the sides. Repeat for second burrito and serve warm.