Spread one teaspoon of butter on one side of each slice of bread. On the other side of each slice, spread one teaspoon of pesto. Top with two slices of Swiss cheese, then avocado slices, and finally a layer of spinach leaves. Place another bread slice on top of stack, butter side up; repeat until you have four sandwiches.
Heat a non-stick skillet until hot. Place sandwiches butter-side down in skillet and cook until browned. Flip and cook until the other side is browned and cheese is melted.
Slice and serve.