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1
Adjust oven rack to middle position and preheat oven to 400u00b0F. Place halved beets in a small baking dish and toss with 1 tablespoon olive oil and salt and pepper to taste. Arrange beets cut side-down and roast until tender, 25 to 30 minutes.
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2
Place lentils and water in a medium pot along with a large pinch of salt. Cover pot and bring to a boil, then drop to a simmer. Cook until lentils are done but still al dente, 30 to 35 minutes. Drain lentils and spread them out in a large bowl to cool.
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3
Meanwhile, heat 3 tablespoons olive oil in a large cast-iron skillet over medium heat until shimmering. Add onion and fennel and cook, stirring occasionally, until vegetables are golden brown and fragrant, about 15 minutes. Chop beet greens, add to skillet and cook, stirring, until wilted, about 8 minutes more. Season mixture to taste with salt and pepper, then scrape mixture into bowl with lentils. Wipe out the skillet.
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4
When beets are cool enough to handle, peel them and cut them into a large dice. Add beets to bowl with lentils.
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5
in a medium bowl, whisk together the mustard, vinegar, honey and salt and pepper to taste. Stream in olive oil, then stir in dill. Add dressing to beets and lentils and stir gently to coat. Turn salad onto a serving platter and scatter feta on top.
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6
Fry eggs: heat 2 tablespoons olive oil in in the cast-iron skillet over medium-high heat until shimmering. Crack one egg at a time into a small bowl, then into pan to fry. Cook, swirling pan so hot oil bastes the tops of the eggs, until egg yolks are barely set, about 4 minutes. Using a thin spatula, transfer fried eggs to top of plated salad and serve immediately.
