Heat a skillet or panini press over medium heat.
Spread the softened butter evenly on one side of each bread slice.
Place two slices of bread, butter-side down, on a clean cutting board. Layer with half of the cheddar cheese, the shredded chicken, the guacamole, and a sprinkle of fresh cilantro.
Top with the remaining cheddar cheese and the other bread slices, butter-side up.
Grill the sandwiches in the preheated skillet for 3 to 4 minutes per side, or until the bread is golden brown and the cheese is completely melted.
Remove from heat, let rest for 1 minute, slice in half, and serve immediately alongside french fries.