Fan out the avocado by removing it from the skin. Cut the avocado at a 45° angle starting ½" from the top, making each slice about a ¼" thick. Sprinkle with salt.
In a hot pan add the oil. Cook tilapia for 3 minutes on each side. Once you flip the tilapia and there is one minute left add the cheese on top of the tilapia. Cover with a lid for the remaining minute. Top with salsa and fanned avocado.