Preheat oven to 200 °C. Trim beef and tie into a neat shape with string. Melt butter in a heavy baking pan on high heat. Cook beef fillet for 6 minutes, turning, until browned. Add brandy and 1/4 cup water and season.
Roast beef for 25 minutes, basting frequently. Remove from oven and cool. Place beef on a piece of foil. Sprinkle with parsley and roll to coat. Leave at room temperature for up to 2 hours before serving.
Meanwhile, make Horseradish Sauce. Combine cucumber, tarragon, sour cream and horseradish in a bowl with vinegar, adding more to taste, if necessary. Stir in snipped chives. Cut beef into thick slices and serve with Horseradish Sauce.