Preheat the oven to 400 degrees F.
Lay the beets on a large sheet of aluminum foil, drizzle with the oil, toss the thyme on top, and season with salt and pepper. Fold up the foil tightly to make a sealed pouch and put it on a sheet pan. Bake until the beets are tender when pierced, about 45 minutes to 1 hour. (Drop a knife in the center of 1 beet; if it slides out without resistance, they're done.) Let the beets cool to room temperature and put them in a large mixing bowl. Add the arugula, celery leaves, and walnuts; toss to combine.
To make the blue cheese dressing: Put the blue cheese and sour cream in a bowl, mashing with a fork to combine. Add the chives, lemon juice, and a few turns of freshly ground black pepper; mix to incorporate, leaving a few chunks of cheese in the dressing. Thin out the dressing with a tablespoon of water, if you wish, to smooth out the consistency.
Pour the blue cheese dressing over the salad and toss gently to coat; season with salt and pepper. Put the salad on a chilled platter and serve.