Using a pastry brush or spoon, slowly brush this 1 buttery glaze over the tops of the slider buns, making sure to cover every roll and letting some of the glaze drip down between the buns and along the sides. This is where the flavor really soaks in, so take your time.
Let the sliders sit for about 10 minutes at room temperature so the buttery glaze can start to soak into the buns. Meanwhile, the oven can finish heating.
Cover the baking dish tightly with aluminum foil and place it in the preheated oven. Bake for 15 minutes, or until the cheese is melted and the sliders are heated through.
Remove the foil and bake for another 8 to 10 minutes, or until the tops of the buns are lightly browned and a bit crisp around the edges, with the buttery glaze bubbling slightly.
Take the baking dish out of the oven and let the sliders rest for about 5 minutes so they’re easier to handle. Using a sharp knife, cut along the bun lines to separate the sliders. Serve warm right from the dish.
For a little sweetness, use Hawaiian rolls instead of plain slider buns; their soft, slightly sweet crumb is a classic Midwestern potluck touch. If you like more bite, add an extra tablespoon of Dijon mustard to the buttery glaze or tuck a few thin slices of dill pickle inside each slider after baking. You can swap the Swiss for provolone, cheddar, or a mix of cheeses, keeping the ham and the same buttery glaze so the recipe still matches the original idea. To make ahead, assemble the sliders and pour the buttery glaze over the buns, then cover and refrigerate for up to 4 hours; let the dish sit on the counter while the oven preheats, then bake as directed, adding a few extra minutes if needed. For a slightly lighter version, use half the butter and brush the glaze on more sparingly, though the full amount gives that rich, old-fashioned flavor. If you’re serving a big crowd, this recipe doubles easily—just use two baking dishes and rotate them in the oven so everything browns evenly.