Cream 1/3 cup butter; add the mustard and garlic, beating well. Spread the butter mixture on one side of the bread slices. Place 1/3 of the bread, buttered side down, in a 13 x 9 x 2 inch baking pan.
Combine 3 cups cheese, onion, salt, and paprika; toss. Set aside.
Melt 1/3 cup butter in a saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add the milk and wine; cook over medium heat, stirring constantly, until the mixture is thickened and bubbly. Gradually stir 1/4 of the hot mixture into the beaten eggs; add to the remaining hot mixture, stirring constantly. Remove from heat.
Top the bread slices in the pan with 1/3 cup cheese; pour half the sauce over the layers. Repeat the layers once; top with remaining bread slices, buttered side up. Sprinkle with the remaining 1/3 cup cheese. Cover and chill at least 8 hours. Bake, uncovered at 350 degrees for 40 to 45 minutes or until lightly browned.