Preheat oven to 400°.
Remove tops of beets. Rinse and tear greens into small pieces, set aside.
Peel and chop beets into 1-inch cubes, then place in a single layer in an 8- by 8-inch baking dish lined with parchment paper and place in oven for 40 to 45 minutes or until fork tender.
During last 5 minutes of baking, heat 2 tablespoons of olive oil in a large skillet over medium heat. Add shallots and sauté for 1 to 2 minutes until translucent. Add beet greens and continue to sauté for an additional 2 minutes until greens have wilted.
Remove beets from oven and add to beet green mixture. Sauté for 1 more minute to combine, then remove from heat. Place sauté mixture in a bowl and mix in basil, goat cheese and salt and pepper to taste.