Heat oven to 400° F. Place the baguette slices on a baking sheet and brush both sides of the bread with 2 tablespoons oil. Bake until golden brown, 4 to 5 minutes per side.
In a small bowl, toss together the artichoke hearts, olives, and parsley with the remaining 3 tablespoons of olive oil; season with ¼ teaspoon each salt and pepper.
Dividing evenly, top the crostini with the artichoke mixture, then the Parmesan.
