1. Brush cut sides of each bun with dressing using a pastry brush. Arrange ham, salami, cheese, lettuce, and tomato on bottom halves of buns. Spread cut side of top halves of buns with spreadable cheese. Place top halves of buns, cheese side down, on each sandwich, pressing gently. Wrap sandwiches individually in plastic wrap, and chill in refrigerator overnight.
2. To serve, unwrap sandwiches, and cut into quarters or halves, if you'd like.