Cut off beet greens, rinse greens well, and pat dry. Remove any tough stems, and then coarsely chop greens. Heat olive oil in a medium nonstick frying pan. Add greens and sauté, stirring frequently, until wilted and tender. Set aside. Peel and thinly slice 3 red beets and 3 golden beets. Sauté golden beet slices until caramelized and tender (note: add additional olive oil to pan if needed). Remove golden beets from pan and set aside, then repeat with red beets.
Sprinkle mozzarella cheese over pizza shell. Arrange beet greens on top of mozzarella. Arrange beet slices decoratively on top of greens. Sprinkle with goat cheese, and season with salt and pepper to taste. Bake pizza on middle rack of oven until dough is crisp and browned, and mozzarella cheese is melted, approximately 8-10 minutes, being careful not to let crust burn. Allow to rest a few minutes before cutting into 8 slices and serving while hot.