For the sauce: Whisk all of the ingredients together in a bowl. Taste and adjust any of the ingredients as needed. Then spread onto both halves of the bread.
Heat a nonstick pan over medium heat. Once hot, add the oil and chorizo. Saute until the chorizo is cooked through while breaking it up into crumbles. Add the eggs and cheese into the pan. Move the eggs using circular motions with a spatula or wooden spoon to fluff up and cook, (move the pan on and off the heat as needed to prevent the eggs from overcooking or drying out). Remove the pan from the heat while the eggs are still moist. Season with pepper. Taste and add salt if needed.
Portion the eggs onto the roll, top with avocado. Cut in half and serve with orange.