Combine all ingredients, except lettuce and avocado in a bowl.
Form into 4-5 patties, place on wax paper.
Cover half of grill with tin foil.
Heat grill to medium heat, brush foil with olive oil and place patties on grill. Place 1 teaspoon of pesto on each patty.
Grill 5 minutes each side, transfer to open grill for 2-3 more minutes, until done.
Serve on lettuce, with avocado slices on top. Wrap up and eat.