In a small bowl combine 4 tablespoons mayonnaise, 2 teaspoons prepared horseradish, 1 teaspoon Dijon mustard, 1 teaspoon lemon juice and 1 teaspoon honey. Stir until smooth.

Season with 1/4 teaspoon salt and 1/4 teaspoon freshly ground black pepper. Taste and adjust: add more horseradish for heat or more honey for sweetness. Refrigerate while you assemble sandwiches (at least 10 minutes).

Sandwich assembly & cooking

Prepare produce

Slice the tomato into 4 even 1/4-inch thick slices. Rinse and pat dry 4 lettuce leaves (butter or romaine work well).

Toast buns

Heat a skillet or griddle over medium heat. Spread about 1/2 tablespoon of the unsalted butter on the cut side of each bun half (use the remaining butter for ham if desired). Place buns butter-side down in the skillet and toast until golden, about 1–2 minutes. Remove and set aside.

Warm ham and melt cheese

Lower heat to medium-low. Add remaining 1.5 tablespoons butter to the skillet and arrange 2 slices of ham per sandwich (8 slices total) in a single layer. Warm the ham 1–2 minutes until edges just begin to brown. Top the ham on each sandwich portion with 1 slice of Swiss cheese (use 2 slices of cheese per sandwich if you prefer heavier cheese). Cover the skillet with a lid or a large bowl to trap steam and melt the cheese, about 1–2 minutes.

If your skillet is small, work in two batches: warm ham and melt cheese for two sandwiches at a time, then repeat.

Assemble sandwiches

Spread about 1 tablespoon of the horseradish sauce on the bottom half of each toasted bun. Place the melted ham and Swiss stack on the sauced bottom bun. Add 1 lettuce leaf and 1 tomato slice on top of the cheese. Spread additional sauce on the top bun if desired, then close the sandwich.

Finish

Serve immediately while cheese is warm. Offer extra horseradish sauce on the side. Leftovers: store components separately in the refrigerator for up to 2 days; reheat ham and cheese briefly in a skillet or oven before assembling.