Place your bread on a cutting board. Mash the avocado and spread on two slices of bread, then layer with the cheese. Spread the pesto on the other two slices of bread. These will make up the top and bottom halves of the sandwich.
Melt half the butter in a nonstick skillet. Place an avocado-cheese half and a pesto half bread-side-down on top of the butter. Cook for about 4 minutes, then close the sandwich with the pesto on top. Griddle for about 2-4 more minutes, or until dark brown, but not black, then flip and griddle the opposite side for another 2-4 minutes. Repeat with 2nd sandwich.
Notes
You can also cook this in a panini press like this awesome Black & Decker 3-in-1 that my mom bought me!! I love it!