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1
Heat the oven to 400 degrees F and arrange a rack in the middle.
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2
Place the beets in an 8-inch square baking dish and add just enough water to cover the bottom of the dish (about 1/3 cup).
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3
Drizzle the beets with olive oil and sprinkle with salt and pepper.
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4
Cover the dish tightly with aluminum foil.
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5
Bake until a knife can be easily inserted into the center of the beets, about 40 minutes to 1 hour 10 minutes (for small beets start checking after 40 minutes; large beets may need even longer than 70 minutes).
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6
Meanwhile, make the creme fraiche dressing and the vinaigrette.
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7
Place the creme fraiche, lemon zest, 1 tablespoon of the lemon juice, and half of the chives in a small, nonreactive bowl and stir to combine.
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8
Taste and season with salt, pepper, and more lemon juice as needed; set aside.
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9
For the vinaigrette, whisk together the mustard, remaining 3 tablespoons lemon juice, vinegar, shallots, and a pinch each of salt and pepper in a small, nonreactive bowl.
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10
Let sit for 15 minutes, then whisk in the measured olive oil in a slow and steady stream; set aside.
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11
When the beets are ready, carefully remove the foil and let them sit until cool enough to handle.
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12
Peel and cut the beets into bite-sized wedges about 1/3 inch wide.
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13
Immediately place them in a large bowl and add the fennel, capers, and remaining chives.
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14
Add the reserved vinaigrette and toss to combine.
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15
Taste and season with salt and pepper as needed.
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16
Just before serving, top with the walnuts and smoked trout, if using.
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17
Drizzle with the creme fraiche dressing.