In a large pot, cover the beets with salted water and bring to a boil. Reduce to a simmer and cook until beets are just tender, about 30 min. Meanwhile, lightly toast the walnuts in a dry skillet over medium heat. Set aside to cool.
Drain the beets and run under cold water until cool enough to handle, but still warm. Gently rub the skins off.
Slice the beets into 1/8-in. (3 mm) rounds and arrange on a platter. Drizzle with the vinegar, olive oil and season with salt and pepper. Sprinkle with the walnuts, cheese and thyme and serve.