Preheat oven to 400 degrees F.
Place artichoke hearts in the center of a clean kitchen towel; gather up the ends and twist firmly to extract all the moisture.
Combine the artichokes, 1 cup Parmesan cheese, mayonnaise, garlic, lemon zest and cayenne pepper in a food processor. Process until smooth, scraping down the sides of the bowl. Season with salt and black pepper.
Spread the mixture in an even layer in a small ovenproof gratin dish. Sprinkle with the remaining 1 tablespoon Parmesan cheese and bake until the top is golden, about 15 minutes. Serve warm.