Preparation:
Line two 9 x 13-inch baking pans with non-stick foil or butter traditional pans.
To prepare marinade, saute minced sweet onion in butter over low heat until onion is soft and translucent. Add poppy seeds, garlic powder, Worcestershire sauce, mustard, and brown sugar. Stir until brown sugar is melted into the sauce. Remove from heat and stir in parsley. Set marinade aside.
Slice the buns in half. Spread bottoms of buns with a thin layer of horseradish mayonnaise. Fold ham slices to fit the bottom of each bun. Repeat with Swiss cheese slices, folding to fit buns. Replace bun tops. Place ham and cheese buns into prepared baking pans. Pour marinade evenly over both pans of buns. Cover tightly with foil. Refrigerate overnight.
Preheat oven to 350 F. Bake marinated buns covered for 25 minutes. Remove foil and bake an additional 10 minutes.
Notes: Use pre-baked dinner rolls. If you make your own yeast dinner rolls, all the better. If you're on a budget, adjust this method to use large yeast hot dog rolls, cut into thirds (you may need to adjust the baking time). Horseradish mayonnaise is easy to make at home, but there are decent commercial varieties to use as a shortcut. You can use regular mayonnaise if you need to avoid horseradish. For the ham, I used a rosemary sun-dried tomato deli ham, but feel free to use your favorite. Just be sure it is sliced very thin and use a high-grade, low-moisture ham for best results.