Preheat broiler and position oven rack to highest position. Arrange baguette slices on a baking sheet and brush with olive oil. Toast under broiler, watching closely and rotating pan as needed for even browning, about 2-3 minutes total.
Let bread cool a bit, then spread evenly with goat cheese. Arrange strawberry slices over top, drizzle with balsamic reduction, and sprinkle with mint or basil leaves.