Whisk the eggs and milk together in a small bowl. Season with salt and pepper.
Melt the butter in a medium non-stick frying pan over low heat. Add the egg and gently push the egg with a flat-bottomed spoon for 3-4 minutes, or until soft folds of cooked egg begin to develop and eggs are cooked as desired. Remove from heat.
Add the avocado to the egg and gently fold through.
Place the tortillas on serving plates. Top with scrabbled egg and fold to enclose filling. Serve immediately.