Preheat oven to 350 degrees. Arrange baguette slices on a large rimmed baking sheet; brush both sides with oil, and season with salt and pepper.
Bake, turning crostini over halfway through, until golden, 6 minutes. Let cool partially on baking sheets.
Once crostini are cool enough to handle, smear one side of the crostini with goat cheese. Top with 2-3 slices of strawberry, sprinkle with chopped basil, and lightly drizzle with aged balsamic. Serve warm or at room temperature.