Melt 3 tablespoons of butter in a small saucepan and add the minced garlic, dried herbs, and salt. Cook on low for 2-3 minutes, until fragrant.
To assemble: Preheat an oven to 400 degrees F. Using the last tablespoon of butter, grease a 9x13 baking dish. Place all the bottoms of the rolls in the baking dish. Layer in the sliced beef, caramelized onions and banana peppers. Top with the provolone cheese. Place the top portion of the slider buns on top. Brush liberally with the garlic and herb butter. Cover with foil and bake for 15 minutes. Remove the foil and bake for another 5 minutes or so, until the tops of the rolls are golden brown and the cheese is melted. Serve immediately with horseradish sauce for dipping.
To make the horseradish sauce: mix all ingredients together and store in an airtight container in the fridge until ready to serve.