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. Spoon the pesto into the cups of an ice cube tray. Tapping the tray gently on the counter to remove any air bubbles. Cover tightly with plastic wrap and place in the freezer. Freeze for 1 day or up to 1 month.
When ready to serve, thaw the pesto. 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.