Preheat oven to 450°F Line a baking sheet with foil; butter or spray foil.
In a shallow dish, combine 1/4 cup of the milk and 1 tablespoons of the mustard. Place cracker crumbs in another shallow dish. Cut chicken breasts into about 3-inch by 1/2 inch strips. Dip each chicken strip first into Milk mixture them into crumbs, pressing to coat. Place on prepared baking sheet. Discard excess Milk mixture and crumbs.
Bake chicken fingers for about 15 minutes or until browned and chicken is no longer pink inside.
Meanwhile, in a small saucepan, whisk flour into remaining milk; whisk in remaining mustard, garlic, salt and pepper. Bring to a boil over medium heat, whisking constantly. Boil, whisking, for about 3 minutes or until thick. Remove from heat; stir in lemon juice and Parmesan cheese. Serve chicken with hot Caesar Dip.
COOKING TIP: Crisp crackers such as Wheat Thins works best. You'll need about 3 cups crackers. Make crumbs in a food processor or place crackers on a resealable plastic bag and crush with a rolling pin.
FOR THE ADVENTUROUS: Add 1/4 teaspoons cayenne pepper to milk for coating mixture and add 1/2 teaspoons anchovy paste and 1 tablespoons chopped drained capers to sauce with garlic.