Cut the tails and leaves from the beets but leave about 1 inch of the stems attached. Wash well and put them in a 2-quart saucepan with enough cold water to cover. Bring to a boil over high heat, reduce the heat to medium low, and simmer until tender when pierced with a skewer, 30 to 35 minutes. Drain and rinse with cold water to cool. When cool enough to handle, slip off the peels. Slice the beets 1/4 inch thick.
While the beets cook, put the potatoes in a 4-quart saucepan with enough water to cover and 1 Tbs. salt. Bring to a boil over high heat, reduce the heat to medium low, and simmer until the potatoes are tender when pierced with a skewer, 20 to 25 minutes. Drain and rinse with cold water to cool. When cool enough to handle, peel and slice 1/4 inch thick.
In a small bowl, whisk the sour cream, horseradish, and vinegar. Mix in the apple and onion, if using. Season to taste with salt, pepper, and vinegar.
In a medium bowl, toss the fennel and parsley with 2 Tbs. of the horseradish dressing, the olive oil, 1/4 tsp. salt, and a pinch of pepper.
Arrange the brisket, potatoes, and beets on 4 large plates. Sprinkle lightly with salt and drizzle with some of the dressing. Pile the fennel on top and serve the remaining dressing on the side.