Whisk mustard with cranberry relish in small bowl; season with salt and pepper.
Arrange bread on flat surface, then evenly spread with mustard mixture. Evenly top 2 of the bread slices with 2 slices of cheese, ham, turkey, remaining cheese and pickles. Top with remaining bread, mustard-side down.
Spread 1 tablespoon mayonnaise on top of each sandwich and cook in medium skillet over medium heat or in panini press, mayonnaise-side down. Arrange brick* on sandwiches in skillet and cook 2 minutes or until the bottoms are golden brown.
Remove brick, then evenly spread tops of sandwiches with remaining 2 tablespoons mayonnaise; turn over. Arrange brick on sandwiches and cook an additional 2 minutes or until bottoms are golden brown and cheese is melted. Cut in half and serve warm.
*Wrap brick in heavy-duty aluminum foil to use as a press.