Adjust racks to top and middle positions and preheat oven to 350 degrees. Wash and dry produce.

Cut potatoes into ½-inch-thick wedges. Drain and roughly chop pickle. Trim and discard root end from lettuce. Dry thoroughly with paper towels; chop into bite-size pieces.

Place 4 TBSP butter (8 TBSP for 8 servings) in a medium microwave-safe bowl and microwave until melted, 30-60 seconds. Add sesame seeds, mustard, and a pinch of salt and pepper; whisk until well combined. 

Toss potatoes on a baking sheet with a large drizzle of oil, Fry Seasoning, salt, and pepper. Bake on top rack until browned and tender, 40-45 minutes.

While potatoes roast, carefully separate top slider buns from bottom slider buns (keep top buns connected and bottom buns connected). Arrange bottom buns in a single layer in a 9-by-13-inch baking dish (two baking dishes for 8 servings).

Evenly sprinkle half the cheddar over bottom buns. Top with ham and chopped pickle. Sprinkle with Monterey Jack and remaining cheddar. Top with top buns to form sliders. 

Spoon sesame mustard butter over sliders (if butter mixture has separated, whisk before using). Cover baking dish tightly with foil. Bake on middle rack for 20 minutes.

While sliders bake, in a large bowl, combine vinegar, half the garlic powder, 3 TBSP olive oil, ½ tsp sugar, and a pinch of salt and pepper (all the garlic powder, 6 TBSP olive oil, and 1 tsp sugar for 8 servings). Whisk until combined.

Add lettuce and coleslaw mix to bowl with dressing. Toss to combine. 

Once sliders have baked 20 minutes, carefully remove and discard foil from baking dish. Return sliders to middle rack and bake, uncovered, until top buns are lightly browned and cheese melts, 5-7 minutes. 

Serve ham and cheese sliders, potato wedges, and salad family style.