In a large pot, place the cubed potatoes, cover with water, and bring to a boil. Reduce the heat to low and simmer for 20 minutes or until the potatoes are tender. Drain the potatoes, reserving 1 cup of the cooking liquid, and return the potatoes to the pot. Add the soy cheese, tofu sour cream, mustard, horseradish, and some of the reserved cooking liquid, and mash until smooth and creamy with a potato masher or whip with an electric mixer. Allow the mixture to cool.
Lightly oil (or spray with a light mist of oil) two non-stick cookie sheets and set aside. Place a star tip in a large pastry bag. Transfer some of the potato mixture to the pastry bag. To form each "nest": in a spiral pattern, pipe a 4-inch circle, then pipe a decorative border all around the inside edge of the circle, and leave the center empty to form a cavity to hold the filling. Chill the potato nests while preparing the filling.
In a saucepan, place the diced beets, cover with water, and bring to a boil. Reduce the heat to low and simmer for 15-20 minutes or until beets are tender. Drain well and set aside. In the same saucepan, saute the onion in olive oil, for 5-7 minutes or until lightly browned and soft. Add the beets and saute an additional 3 minutes. Add the remaining ingredients, stir well to combine, and simmer for 3-4 minutes or until the sauce is reduced to a glaze on the beets. Taste and adjust seasonings as needed. Cover, remove from the heat, and set aside.
Remove the potato nests from the refrigerator and allow them to warm up for 5 minutes. Then in batches, place each of the cookie sheets under the broiler for 4-5 minutes to lightly brown the tops of each potato nest. Carefully fill each of the browned potato nests with the warm beet filling. Using a spatula, transfer the nests to a large platter for service. Serve one potato nest per person. Individual servings can be garnished with a dollop of tofu sour cream and a few snipped chives, if desired.
*The potato nests can be preshaped and chilled ahead of time. The beet filling can also be prepared ahead but should be kept separately. Allow both of them to sit at room temperature for 10 minutes, then simply fill the nests and place them under the broiler for 5-7 minutes or until lightly browned on top.
Serves 10