Spread layer of goat cheese over both slices of bread. Slice strawberries relatively thinly. Spread strawberries over one slice of bread, and basil on other. Sprinkle both sides with black pepper, and lay basil slice face down on top of strawberry slice.
Heat small-to-medium skillet (cast iron is best) over medium heat. Melt 1—2 teaspoons of butter in skillet. Add sandwich. Cover with a plate or appropriately sized dish and weigh it down with something heavy, like canned beans or a cast iron skillet. Cook until bottom of bread is lightly browned, about 2—3 minutes. Remove from pan. Add another pat of butter, let it melt, and return sandwich to repeat on other side. Slice in half and serve warm.
To make balsamic honey sauce, combine balsamic vinegar and honey in small saucepan over medium-low heat. Simmer, stirring constantly, until liquid is reduced by about half (15 minutes or more). Pour liquid into a small bowl to cool.
Recipe courtesy of Cookie and Kate