Place a large pasta pot over high heat and fill it with the wine (add additional water as needed to fill it up to your normal level for preparing pasta). Salt the liquid liberally and bring it to a boil.
Clean the stem and root ends of the beets and reserve the greens to add to your salad. (Rub your hands with a little oil so the beets will not stain your hands and work on a rubber board so they don’t stain your counter.) Peel the beets with a vegetable peeler then grate them with a box grater.
Give your hands a good wash then place a large skillet over medium to medium-high heat with 3 turns of the pan of EVOO, about 3 tablespoons. When the pan is hot, add the beets and garlic, and sauté until the beets are tender, 8-10 minutes.