Place parsley, garlic, chilli and pistachios in a food processor. Process until finely chopped. Add juice, oil and avocado and process until combined. Add ¼ cup (60ml) water and process until combined. Season.
Heat a large frying pan over medium heat. Add chorizo and cook, turning, for 5-7 minutes or until golden and heated through. Transfer to a paper towel lined plate.
Whisk eggs with salt and pepper. Drain excess oil from pan. Reheat pan over medium-high heat. Pour half the egg mixture into pan to create a thin omelette. Cook for 2 minutes or until set. Repeat with remaining egg mixture. Cut omelettes into strips.
Fill rolls with omelette strips and chorizo. Spoon over sauce, then scatter with tomatoes and parsley leaves. Serve.