
In a blender, puree drained artichoke hearts, garlic, vinegar and 1/2 cup olive oil. Season with salt and pepper. Refrigerate if making ahead.
To make crostini from baguettes, preheat oven to 350 degrees. Place 1/2-inch slices baguette on parchment paper-lined baking sheets; brush olive oil lightly on both sides of each slice. Bake about 7 to 10 minutes, until lightly toasted.
Remove from oven; cool crostini on wire rack.
Spread each slice with a generous slathering of artichoke puree; top puree with some of the shredded arugula, followed by thinly sliced beef.
Use a vegetable peeler to make curls of cheese from the wedge of parmesan; top each crostini with a curl. Serve at room temperature.
Note: Buy two baguettes in case arge air bubbles are lodged in the middle of some slices.