Preheat the oven to 425 degrees F.
Cut the greens off the beets and slice them into 1/2-inch pieces; reserve. Trim and discard the beet stems. Combine the beets, 2 tablespoons of the oil, 1 teaspoon salt, some pepper, 5 of the thyme sprigs and the garlic cloves on a baking sheet. Cover with foil and roast for 30 to 35 minutes, until easily pierced with a paring knife. Set aside to cool completely.
Meanwhile, toast the pistachios in the oven for 5 minutes. Let cool.
Melt the butter in a medium saucepan or lidded deep skillet over medium heat. Add the farro and toast for 2 minutes--the color will darken slightly and the farro will acquire a nutty fragrance. Add 2 cups water, 1 teaspoon salt and the remaining 5 thyme sprigs. Bring to a boil, then reduce to a simmer. Cover and cook for 25 minutes, or until al dente (cooked but still firm to the bite). Drain the farro well and pour into a serving bowl.
While the farro is still hot, add the beet greens, tossing to allow the heat to wilt the greens. Set aside to cool completely.
With a paper towel, remove the skins from the beets. Quarter the beets and add them to the bowl with the farro. Fold in the toasted pistachios.
Squeeze the roasted garlic into a small bowl. Mash with a fork and season with salt and pepper. Add the vinegar and then whisk in the remaining 2 tablespoons olive oil. Adjust the seasoning as desired.
Pour the dressing over the salad and toss gently to combine. Top with the crumbled goat cheese.