Fried Mac And Cheese Bites

Name: Fried Mac And Cheese Bites
Ingredients: 1 Tbsp. unsalted butter; 0.33 cup (about 1 1/2 oz.), plus 1 Tbsp. all-purpose flour, divided; 1.25 cups whole milk; 8 oz. white Cheddar cheese, shredded (about 2 cups); 8 oz. Monterey Jack cheese, shredded (about 2 cups); 2 tsp. kosher salt; 1 tsp. garlic powder; 0.5 tsp. black pepper; 0.5 tsp. cayenne pepper; 8 oz. elbow macaroni, cooked according to pkg. directions; Vegetable oil; 2 large eggs, lightly beaten; 2 Tbsp. water; 2.5 cups panko (Japanese-style breadcrumbs)