In a small pot over medium heat, melt 3 tablespoons butter. Add garlic, sauté 2 minutes then whisk in flour and cook 1 minute. Whisk in about 1 1/4 cups milk and let thicken 1 minute. Season with salt and pepper. Stir in mustard and turn off heat.
Spread yellow mustard béchamel on 8 slices of bread. Build sammies with 2 slices Swiss, ham, turkey or pork and sliced pickle. In a shallow dish, whisk together eggs and remaining 1/4 cup milk.