Make Balsamic honey sauce. Combine the balsamic vinegar and honey in a small saucepan over medium-low heat. Simmer, stirring constantly, until the liquid is reduced by about half (15 minutes or more). Pour the liquid into a small bowl to cool.
Make Sandwich. Spread a layer of goat cheese over both slices of bread and sprinkle both sides with black pepper. Top one slice with raspberries. Sprinkle with basil, and top with remaining bread.
Heat a skillet to medium heat. Melt one to two teaspoons of butter in the skillet, then add the sandwich. Cover it with a plate or appropriately sized dish and weigh it down with something heavy, like canned beans or a cast iron skillet. Cook for 1-2 minutes or until the bottom of the bread is lightly browned.
Lift the sandwich from the pan, add another pat of butter, let it melt, and return the sandwich to cook on the other side.
Slice sandwich in half and serve warm with a side of balsamic honey sauce.