Prepare a moderately hot charcoal fire in a grill unit that has a cover. Place beets and red onions in a 10 inch cast iron skillet and drizzle with olive oil. Place skillet on grill rack over fire, cover the grill unit and roast the vegetables 1 to 1 1/2 hours, depending on the size of the vegetables. You may have to cook the beets a little longer than the onions. The onions should be soft to the touch and a fork should pierce the beets easily.
Alternately, you can roast the beets in a skillet in a preheated 400° F. oven. Remove vegetables from skillet with tongs.
Add broth, vinegar and 1 teaspoon thyme to the skillet, place over high heat and boil liquid, scraping bottom of skillet for about 4 minutes or until it’s dark, glossy brown and syrupy. Season with salt and pepper.
Peel beets and onions when they’re cool enough to handle. Slice the beets into julienne strips and onions into thin rings.
Spoon liquid over onions and beets, add remaining 1/2 teaspoon thyme and stir well to combine. Heat briefly and serve.
