In a food processor combine the artichokes, parsley, walnuts, lemon zest and juice, garlic, salt, and pepper. Run the machine to finely chop all the ingredients, stopping the machine a few times to scrape down the sides.
Then, with the machine running, drizzle in 1/2 cup extra-virgin olive oil.
Mix in the Parmesan.
Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
Drizzle the ciabatta slices with the 1/4 cup extra-virgin olive oil. Grill until toasted, about 5 minutes.
Spread the artichoke pesto over the toasted slices and serve.