Preheat oven to 350 degrees. Make crostini. Brush baguette slices on both sides with olive oil; season with salt and pepper. Place on a baking sheet and bake, turning once, until golden, 10 to 12 minutes.
Meanwhile, make topping. Finely chop artichokes, and combine in a bowl with Parmesan, parsley, and remaining tablespoon oil.
Dividing evenly, spoon topping onto crostini, and garnish with additional Parmesan, if desired.