1. Melt butter in a small saucepan over medium heat; slowly bring to a boil, skimming froth from surface. Carefully pour melted butter into a small bowl, holding back the milky sediment in the bottom of the pan. The clarified butter should be the color of light olive oil; let cool to room temperature.

2. In a medium heavy-bottomed saucepan, mix vinegar together with 1/4 cup cold water and crushed peppercorns. Place over medium-high heat until liquid is reduced by one-third; remove from heat and let cool completely. Add egg yolks to cooled reduction and whisk to combine.

3. Place saucepan on a heat diffuser over very low heat; whisk, making sure the whisk comes in contact with the bottom of the pan. Gradually increase heat whisking, so the sauce emulsifies progressively and becomes smooth and creamy, 8 to 10 minutes; do not let the temperature of the sauce rise above 150 degrees.

4. Remove saucepan from heat and whisk in clarified butter in a slow, steady stream; season with salt. Stir in lemon. Line a chinois or fine mesh strainer with cheesecloth; strain mixture and discard solids. Mix together mustard powder and water; stir into hollandaise sauce along with horseradish. Use sauce immediately.