Lightly toast hazelnuts in a dry skillet set over medium heat, 4 to 5 minutes. Let hazelnuts cool to room temperature, then pulse in a food processor until finely chopped.
To the food processor, add artichoke hearts, garlic, and Parmesan cheese. Pulse until smooth. With the food processor running, slowly add olive oil. Process until the olive oil is combined well with the artichoke mixture.
Stir in 2 tablespoons chopped fresh parsley. Serve with crackers, small toasts, or raw vegetables.