Heat oil in a large pot over medium heat. Add onion and a pinch of salt; cook and stir until onion is softened and translucent, 5 to 10 minutes. Add garlic and ginger; cook and stir until fragrant, about 1 minute. Add beets and stir to combine. Add 1 cup water and 1/2 teaspoon salt; bring to a boil.
Cover the pot and reduce the heat to medium-low. Simmer, stirring occasionally, until beets are easily pierced with a fork, 20 to 25 minutes. Add potatoes and cook until potatoes are soft but not falling apart, about 15 minutes.