Mash the potatoes thoroughly using a potato masher, or for a professional-grade smooth texture, force them through a food mill or a potato ricer into a large mixing bowl.
Incorporate 4. 0 tbsp (56. 0g / 0 oz) of unsalted butter, 2. 0 tsp (10. 0g / 0 oz) of freshly grated horseradish, 1. 0 tsp (5. 0g / 0 oz) of salt, and 0. 125 tsp (0. 5g / 0.18 oz) of white pepper.
Use a fork to vigorously mash the mixture until all ingredients are well blended and the butter is fully incorporated into the potato base.
Allow the mixture to cool completely at room temperature before handling to ensure the balls hold their shape.
Divide the mixture into 12. 0–15. 0 equal portions and, using buttered palms to prevent sticking, roll each portion into a smooth, uniform ball.
Arrange the balls on a serving platter and sprinkle lightly with 0. 125 tsp (0. 5g / 0.18 oz) of paprika or cayenne pepper for a pop of color and heat.
When rolling the balls, keep a small bowl of melted butter nearby to lightly grease your palms; this ensures a smooth, professional finish without the potato sticking to your skin.