Wash the beets and greens, leaving the skins on. Remove the greens close to the roots, take off the stems and tear the beet greens into 2-inch pieces. Put aside.
Drop the beets in salted boiling water and let simmer until tender, for 25 minutes. Drain the water and let them cool in cold water. Peel by rubbing them with a rag. Put aside. You can also use a peeler.
When the beets are done, heat the olive oil in a skillet over medium-low heat. Add the shallot, garlic and beets and cook for 5 minutes. Add the red chard and the beet greens and cook for 1 minute, until the greens wilt. Add the butter and a little water and season with salt and pepper. Keep warm and serve with fried skate.