Open-Faced Burgers with Horseradish-Cheese Sauce

1 garlic clove, minced and mashed to a paste with
1/2 teaspoon salt
1 Tablespoon unsalted butter
1 kaiser roll, halved
1/3 cup sour cream
1/2 cup grated extra-sharp Cheddar
1 Tablespoon drained bottled horseradish
1 Tablespoon minced bottled sweet pickle
1 teaspoon minced bottled pickled jalapeno chili (wear rubber gloves)
1 Tablespoon vegetable oil
3/4 pound ground chuck, formed into two 1/2-inch-thick patties

In a small saucepan combine the garlic paste and the butter and heat the mixture over moderately low heat, stirring, until the butter is melted. Brush the cut sides of the roll with the butter mixture and toast the roll halves lightly. In a saucepan combine the sour cream and the Cheddar, heat the mixture over moderately low heat, stirring occasionally, until the cheese is melted, but do no let it boil, and stir in the horseradish, the pickle, and the jalapeno chili. In a heavy skillet (preferably cast-iron) heat the oil over moderately high heat until it is hot but not smoking and in it cook the patties, seasoned with salt and black pepper, turning them once, for 8 minutes for medium-rare meat. Transfer the burgers to the roll halves and spoon the horseradish-cheese sauce over them. Serves 2.