Sauté first 3 ingredients in a lightly greased skillet over medium-high heat 8 minutes or until onion is tender.
Spread 1 tablespoon horseradish sauce on each of 4 bread slices; top evenly with roast beef, cooked onion, and cheese. Top with remaining bread slices. Brush melted butter on both sides of sandwich.
Cook in a preheated panini press 2 to 3 minutes or until golden brown. Serve with remaining horseradish sauce.