Bring 4 c. water to a boil in a large saucepan. Add potatoes; cook 5 to 7 minutes. Drain, pat dry, and cut potatoes into rounds 1/4" thick. Spray with approximately 1.5 oz. olive oil spray, or brush with 2 Tbsp. of olive oil if using liquid version. Sprinkle potato rounds with 1-2 Tbsp. of horseradish, as desired.

While the potatoes are boiling, coat grill rack of outdoor grill with nonstick cooking spray and preheat it to medium low (250-300°F) to prevent potatoes from burning. If you don't have an outdoor grill, you can grill potatoes in a grill pan over medium heat.

Depending on your grill and your desired temperature, grill potatoes for about 10-15 minutes or until browned on the edges and tender, turning occasionally. Place the potatoes on a wire rack to cool slightly, then transfer to a large mixing bowl.

Combine vinegar, 4 Tbsp. olive oil, mustard, onion, remaining 1 Tbsp. horseradish, lemon zest, parsley, and red pepper flakes in a small bowl. Add to potatoes, stirring well. Serve warm or chilled.