In a small bowl combine 1/2 cup mayonnaise, 2 tablespoons ketchup, 2 tablespoons sweet pickle relish, 1 teaspoon white wine vinegar, 1/4 teaspoon Worcestershire sauce, 1 teaspoon hot sauce, 1/2 teaspoon sugar (if using), 1/4 teaspoon salt and 1/8 teaspoon black pepper. Whisk thoroughly until smooth and uniform. Taste and adjust seasoning (add more vinegar for tang, more relish for sweetness). Refrigerate while you assemble the sandwich so flavors meld (at least 10 minutes, up to overnight).

Sandwich

Prepare roll

Preheat broiler or a skillet over medium heat if you prefer to toast. Slice the hoagie roll open lengthwise, leaving a hinge if desired. Lightly spread the cut interior with the softened butter and sprinkle the butter with the optional 1/8 teaspoon garlic powder. Toast under the broiler for 1–2 minutes until lightly golden, or toast in the skillet cut-side down for 1–2 minutes.

Layer meats and cheese

On the bottom half of the warmed roll, layer the 4 slices salami evenly, then the 3 slices ham, and top with the 3 slices pastrami. Place 2 slices provolone cheese over the top of the pastrami. If you like the cheese melted, place the assembled bottom half under the broiler for 30–45 seconds or cover the skillet with a lid until the cheese softens.

Assemble vegetables

On the top half of the roll spread 2–3 tablespoons of the prepared Thousand Island dressing evenly. Over the dressing, add 1/2 cup shredded iceberg lettuce, 3 thin tomato slices, and 3 red onion rings if using. Add dill pickle slices if desired.

Finish sandwich

Close the sandwich, pressing gently to compress the fillings. Cut in half on a sharp diagonal if desired. Serve immediately so the toasted roll stays crisp and the cheese remains warm. Provide extra Thousand Island dressing on the side if desired.