In a small bowl, stir together all the ingredients for the dip. Cover it with plastic wrap and refrigerate until ready to use.
Heat the oven to 425°. Cover a baking sheet with foil. Coat the foil with cooking spray.
Place three shallow pans (such as cake pans) in a row. Fill the first with the flour; mix the eggs and milk in the second; and whisk together the cheese, bread crumbs, garlic powder, and salt in the third. Place the prepared baking sheet at the end of the row.
With clean hands, dredge the beans, a few at a time, in the flour, then the egg mixture, then the cheese mixture, tossing them gently to coat them completely. Once coated, place them on the baking sheet.
Bake the beans until lightly golden brown, about 12 minutes. Let them cool slightly before serving with the dip.