Grate beets and carrots on the large holes of a box grater set in a large bowl (or shred in a food processor). Stir in chickpeas, potato, flour, and 1 teaspoon salt. Season with pepper. In a large nonstick straight-sided skillet, heat 1 tablespoon oil over medium. Add beet mixture and, with a rubber spatula, firmly press evenly into pan. Cook, undisturbed, 10 minutes. Remove pan from heat, cover with a serving platter, and carefully invert pancake onto platter. Slide pancake back into pan and cook until crisp and brown around edge, 10 to 12 minutes. Invert pancake onto platter.