Lay baguette slices on a work surface and spread mustard on one side of each slice. Layer ham, turkey and cheese evenly on each of 12 bread slices, then cover with remaining bread slices to make 12 small sandwiches.
Beat eggs and 1/4 cup water in a wide, shallow bowl. Add sandwiches, two at a time, and turn in egg mixture to coat thoroughly. In a large nonstick skillet, melt 2 Tbsp. butter over medium heat.
Add 6 sandwiches to skillet, cover and cook until golden on bottom, about 4 minutes. Turn and cook until golden on other side, about 3 minutes longer. Keep sandwiches in a warm oven while you repeat process with remaining butter and sandwiches. Serve with jam or syrup for dipping.