Preheat oven to 400°.
Combine first 4 ingredients in a food processor; add 1 can of artichokes and beans. Process until smooth. Add remaining can of artichokes, 3/4 cup of Parmigiano-Reggiano cheese, 1 tablespoon parsley, and garlic. Pulse 20 times or until artichokes are coarsely chopped.
Spoon mixture into an 8-inch square baking dish coated with cooking spray; sprinkle top with remaining 1/4 cup of Parmigiano-Reggiano cheese and remaining 1 tablespoon parsley. Bake at 400° for 25 minutes or until bubbly.