Put the beet juice in a small, heavy-bottomed saucepan and bring to a boil over medium-high heat. Reduce the heat to maintain a simmer and simmer for about 25 minutes or until the juice is reduced to a syrup. Remove from the heat.
Strain the reduction through a chinois or fine-mesh sieve into a small bowl. Cover and refrigerate until needed.
Preheat the oven to 375 degrees F. Lay out a large piece of aluminum foil. Make a 1/2-inch thick bed of kosher salt on a jellyroll pan.
Rinse and dry the beets. Remove all but 1 inch of the stems (leaving the roots and part of the stems prevents the beets from bleeding). Coat the beets with 1 tablespoon of the olive oil and place them on the jelly-roll pan. Wrap the beets with the foil to form a package and set it on the bed of salt.
Roast the beets for 30 to 40 minutes or until tender. To test for tenderness, insert a skewer or paring knife into 1 of the beets. If the skewer meets with no resistance, the beets are done.
When the beets are cool enough to handle, cut off the roots and stems. If you wish, keep the stems on a few beets for presentation. Slip the skins off the beets with your fingers.
Cut the beets into quarters and put them in a medium-sized bowl. Toss with the remaining olive oil and season, to taste, with salt and pepper.
To serve, place a few assorted beet quarters inside a small cup, positioning the ones with stems near the top. Drizzle with the red beet juice reduction and garnish with thyme leaves. Repeat to make 5 more servings.
Note: 12 ounces of beets make about 3/4 cup juice.
Recipe courtesy of Rick Tramonto, Amuse-Bouche: Little Bites That Delight Before the Meal Begins, Random House, October 2002