Mix ground beef with remaining 1 tbsp. steak sauce and smoked paprika. Season with salt and pepper. Shape into 4 patties.
In a large skillet, melt Finlandia butter, then add mushrooms. Cook until lightly golden brown, then add onions and jalapeño pepper. Continue to cook until onions start to caramelize and mushrooms are well browned. Season with salt and pepper.
Cook burgers on each side until desired doneness. Remove from heat. Top with Finlandia Swiss Cheese and hot mushrooms and onions. Serve on a bun with steakhouse mayo.