Prepare beet tops: Cut beetroot from the stem. Cut the beet greens from the stems and place in a colander or bowl to wash, rinse well to remove excess dirt, then set aside to dry.
Prepare and simmer soup: To a large soup pot over medium heat, add oil. After oil is heated, add cut beetroot, diced onion, celery slices, and sliced carrots to the pot and cook until onions and celery start to soften and carrots begin to brown, about 5 minutes. Add minced garlic and cook 2 minutes more, until it begins to brown and become fragrant. Add bay leaves and vegetable broth, white beans, and a pinch of salt and pepper and increase heat to high and bring to a boil, then reduce heat to a simmer and cook for 30 minutes.
Serve soup: When soup has cooked for 30 minutes, remove from heat and stir in beet greens. Add red pepper flakes and more salt and pepper to taste.
Slow cooker instructions: Add the oil, onion, celery, carrots, white beans, bay leaves, broth, and salt and pepper to the pot. Cook on medium for 1 hour, then stir in beet leaves and season to taste before serving.
Pressure cooker instructions: Add the oil, onion, celery, and carrots to the pot and, using sauté setting, cook until vegetables begin to soften. Then add the beans, bay leaves, broth, salt, and pepper, and cook on the high pressure soup setting for 10 minutes. Remove lid carefully, stir in the beet greens, and season before serving.