Preheat the oven to 350°F. Line a baking sheet with enough aluminum foil to double over itself. Place the beets in the middle of the foil, scatter the thyme and 4 teaspoons salt over them, then wrap the beets tightly in the foil. Bake until easily pierced with a fork but still slightly firm, 1 hour to 90 minutes, depending on size. Let cool. Unwrap, remove, discard the skins, and cut the beets into bite-size pieces.

Meanwhile, in a saucepan over medium heat, mix together the balsamic vinegar, olive oil, sugar, and 1 teaspoon salt. Add the shallot slices, turn the heat to low, and cook, stirring occasionally, until all the vinegar evaporates, about 1 hour. (Don’t worry if the oil and vinegar separate.) Set aside.

Meanwhile, spread the walnuts in one layer on a baking sheet and toast until lightly browned, 10 to 15 minutes. Let cool.

In a frying pan over medium heat, toast the buckwheat, stirring occasionally, until it gains some color, about 4 minutes. Let cool.

Mix the shallot-balsamic dressing to combine. In a bowl, toss the beets with just enough of the dressing to coat. Season to taste with salt and pepper. Top with the buckwheat, flax seeds, walnuts, and cheese, garnish with the orange segments, and serve.