Not only is this ruby red side dish a showstopper. It's also packed with betalains, red and yellow pigments that act as antioxidants that search for and stabilize free radicals (which can cause cell damage).
Preheat the oven to 425 degrees F. Put the fennel in a medium bowl, cover with ice water and set aside.
Put the beets in a 3-quart casserole dish and toss with the chicken broth, 1 tablespoon of the olive oil, 1/2 teaspoon salt and a few grinds of pepper. Cover the dish with foil and bake for 45 minutes. Remove the foil; if there is 1/4 inch or less of liquid, add 1/2 cup of warm water. Continue baking, uncovered, until the cooking liquid is reduced by half and the beets are fork-tender, 25 to 30 minutes.
Meanwhile, whisk the vinegar, butter, remaining 2 tablespoons oil and mustard in a measuring cup. Strain the fennel and toss with the vinegar mixture in a large bowl. Add the dressed fennel to the beets, toss with tongs and continue baking until the fennel is crisp-tender, about 15 minutes. Remove the dish from the oven, stir the beets and fennel to coat with the sauce and season with 1/4 teaspoon salt and a few grinds of pepper. Transfer to a serving bowl and garnish with the chives.
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