Preheat the oven to 425 degrees F.
In a roasting pan, toss the beets with the salt, pepper, 3 tablespoons sherry vinegar and 3 tablespoons olive oil. Cover with foil and roast for 1 hour.
Remove the beets from the oven and allow to cool slightly. Using several paper towels and with rubber gloves, peel the skins off the beets, keeping the yellow and red beets separate. Cube the red beets on a cutting board lined with parchment paper into 1/2-inch pieces. Put into a bowl and set aside. Repeat with the yellow beets and put into a separate bowl.
Lower the oven temperature to 300 degrees F.
In a medium-sized saucepan, bring the water, sugar and walnuts to a boil over medium heat. Drain the walnuts and put them on a sheet pan lined with lightly greased parchment. Bake in the oven until well toasted, about 12 to 15 minutes. Remove from the oven and allow to cool.
Divide the shallots and thyme between the red and yellow beets.
Season each set of beets with sherry vinegar, olive oil, salt and pepper. Arrange the beets on a large serving platter keeping the beets separate for presentation. Top with crumbled goat cheese and candied walnuts.