Prep: Cut the mozzarella into slices and place them on a few layers of paper towels. Dab each slice and allow them to sit for about 10 minutes before you make your sandwich to remove excess moisture.
Outside: Spread olive oil onto the outward facing side of each piece of bread.
Avocado: Onto the inside of each piece of bread, evenly mash avocado so that it is spread all over the inside of the bread. This will keep the sandwich from becoming soggy when cooked!
Fillings: Onto one of the pieces of bread, pile on chopped strawberries, mozzarella, and basil. Sprinkle with salt and pepper. Set remaining piece of bread with mashed avocado on top.
Cook: Cook in a pan or panini press on medium heat for about 5 minutes, flipping halfway through, or until everything is melted and hot. Optionally serve with balsamic mayo.