This recipe leaves little to waste by employing the beet greens in the bulgur and the pan drippings in the vinaigrette. Substitute shredded kale if using loose beets.
Preheat oven to 450 degrees. Place lemon slices on a rimmed baking sheet; drizzle with oil. Top with chicken; season with salt and pepper. Roast until a thermometer inserted into thickest parts of chicken (avoiding bones) registers 160 degrees, 30 minutes. Whisk 1 tablespoon water into pan juices; reserve. Meanwhile, place bulgur and 1 teaspoon salt in a bowl; add boiling water to cover by 1 inch. Cover and let stand until tender, 20 minutes. Drain.
Heat oil in a skillet over medium-high. Add beet tops, shallots, and a pinch of salt; cook 3 minutes. Stir in bulgur. In a bowl, combine lemon juice and Dijon; whisk in reserved pan juices. Season with salt and pepper. Remove chicken from bones; slice. Divide bulgur mixture among bowls; top with carrots, grated beets, yogurt, and chicken. Drizzle with dressing and serve.