Place half the artichokes in a food processor; add cream cheese, 1/4 cup Parmesan, lemon juice, garlic, cayenne, and 3 tablespoons water. Process until smooth.
Add scallions, remaining artichokes, and spinach; pulse briefly. Transfer mixture to a serving bowl. (To store, refrigerate, up to 2 days.) Top with 1 tablespoon Parmesan, and serve dip with raw vegetables.