Preheat oven to 350 degrees. Make crostini: Brush baguette slices on both sides with a total of 1 tablespoon oil; season with salt and pepper. Place on a baking sheet, and bake, turning over once, until golden, 10 to 12 minutes. Cool.
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.