Preheat the oven to 400 degrees F.
Trim the beet stems. Put the beets on a large piece of aluminum foil, drizzle with olive oil, and seal the foil to make a tight package. Transfer to small roasting pan. Roast the beets until they can be easily pierced with a knife, about 1 hour. When cool enough to handle, rub or peel off skins.
Meanwhile, halve and very thinly slice the fennel (we love a mandolin for this). Soak in cold water to crisp. Segment the grapefruits over another bowl, reserving the juice. Cut the segments in half.
Whisk 2 tablespoons of the reserved grapefruit juice with the mustard, vinegar, honey, and 1/2 teaspoon salt in a medium bowl. Gradually add the oil in a steady stream to make a creamy dressing. Season with pepper to taste.
Thinly slice the beets with a knife or on a mandolin and toss in a bowl with 3 tablespoons dressing. Season with salt and pepper to taste and arrange on individual plates. Drain the fennel, dry well. Just before serving, toss the fennel, lettuce, grapefruit, and tarragon with dressing. Divide evenly and set on beets. Serve immediately.
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