Primanti-Style Sandwiches

½ cup mayonnaise

2 tablespoons milk

1 tablespoon white vinegar

½ teaspoon white sugar

6 cups shredded cabbage

3 cups olive oil

4 potatoes, sliced 1/4 inch thick

¼ pound thinly sliced capicola

4 (1 ounce) slices mozzarella cheese

4 (1 ounce) slices provolone cheese

4 (1 ounce) slices Swiss cheese

8 thick slices Italian bread

4 thin slices onion

4 thin slices tomato

Whisk together the mayonnaise, milk, white vinegar, and white sugar in a large bowl; add the cabbage and toss to coat. Chill in refrigerator at least 1 hour.

Heat oil in deep-fryer or large deep pan to 375 degrees F (190 degrees C); add the potato slices; cook until crispy and golden brown, 5 to 6 minutes. Drain on paper towels.

Place a large skillet over medium heat. Arrange the capicola in four separate stacks in the skillet and top each stack with 1 slice mozzarella cheese, provolone cheese, and Swiss cheese; heat until the cheese begins to melt.

Arrange 4 slices of Italian bread on 4 separate plates. Top each slice with a stack of capicola and melted cheese; about 1 1/2 cups of the cabbage mixture, 1 slice onion, 1 slice tomato, and about 1/4 of the fried potatoes. Top with the remaining bread slices. Cut each sandwich in half to serve.