Place the beets in a saucepan with water; bring to a boil over medium-high heat and cook until tender, 10-15 minutes. Drain the beets, then peel and halve or quarter them.
Place the sugar in a skillet and add a little water so that it looks like wet sand. Bring to a boil, then simmer to evaporate the water out. When the sugar begins to color, remove it from the heat so that it won’t spatter and gently whisk in the vinegar. Return the skillet to the heat and thicken the mixture to coat the back of a spoon. Remove the mixture from the stove and stir in the horseradish. Whisk in the EVOO and season with salt and pepper. Toss the beets with the sauce and the parsley and serve.