Slice the chicken breast fillet horizontally to make two thin fillets. If you wish, you can cook both pieces and make two crumpets to serve two people, or allow one piece of chicken to cool then cover and refrigerate to use the following day.
Heat a griddle pan or frying pan until hot. Drizzle a little olive oil over the chicken and rub to coat evenly then season with black pepper.
Once the pan is hot, carefully place the chicken into the pan and allow to cook for about 3 minutes then turn and cook for a further 2-3 minutes.
Add the asparagus to the side of the pan for a couple of minutes whilst the chicken is finishing. Check that the meat is cooked and the juices run clear then lift onto a plate. Remove the asparagus and set aside with the chicken.
Toast the crumpet(s). Slice the avocado and arrange on top of the crumpet then top with the warm chicken and serve with the asparagus on the side.