1. Preheat oven to 350°. Generously grease 2 (12-cup) miniature muffin pans. Pick crabmeat, removing any bits of shell.
2. Stir cream cheese in a large bowl until smooth. Add 1/3 cup Parmesan cheese and next 6 ingredients; stir until smooth. Fold in crabmeat and parsley.
3. Combine remaining 1/3 cup Parmesan cheese, breadcrumbs, and melted butter in a medium bowl; toss with a fork until breadcrumbs are moistened. Spoon 1 Tbsp. breadcrumb mixture into each muffin cup; press into bottom and up sides to form crust. Spoon 1 Tbsp. crab mixture into each crust.
4. Bake at 350° for 25 minutes or until golden brown. Cool in pans 5 minutes. Run a knife around edges of crab cakes to loosen; gently lift cakes from pan. Serve warm or at room temperature topped with Chive Aïoli.