Preheat the oven to 425°F.

Peel the beets and cut them into 1-inch wedges.

Discard the tough stems from the beet tops and coarsely chop the leaves.

In a bowl, toss the golden beets with 1 teaspoon of olive oil and 2 garlic clove halves and season with salt and pepper.

Arrange the golden beets in one-third of a large ovenproof skillet.

Repeat with the red beets, using 1 teaspoon of olive oil and 2 garlic halves for each vegetable, and arrange them in the skillet.

Repeat with the carrots, using 1 teaspoon of olive oil and 2 garlic halves for each vegetable, and arrange them in the skillet.

Set the skillet over high heat and cook without stirring until sizzling.

Cover the skillet and roast in the oven for about 35 minutes, until the vegetables are tender.

Transfer the roasted vegetables to a platter.

In a small bowl, whisk together the sherry vinegar, 1 tablespoon of olive oil, and half of the minced shallot.

Season the vinaigrette with salt and pepper.

Whisk in the crumbled goat cheese into the vinaigrette.

In the same skillet, heat the remaining 1 tablespoon of olive oil over moderately high heat.

Add the remaining minced shallot to the skillet and cook until softened, about 1 minute.

Add the chopped beet greens to the skillet and cook until just wilted, about 5 minutes.

Season the beet greens with salt and pepper.

Add half of the goat cheese dressing to the beet greens and toss to combine.

Add the roasted vegetables to the skillet and toss once or twice.

Transfer the salad to a platter and drizzle with the remaining dressing.

Serve immediately.