Trim the tops and bottoms of your beets, leaving the skins intact. Place them in a large pot and cover with water. Add a tablespoon of vinegar to the cooking water to preserve color.
Bring to a boil, then reduce heat and simmer until tender when pierced with a fork, approximately 30-35 minutes.
Once cooked, drain the beets and let them cool until you can handle them comfortably. The skins should slip off easily when rubbed gently with your fingers or a paper towel.
Cut the peeled beets into chunks and place them in a blender with 1 cup of vegetable broth. Blend until smooth and velvety. Add more broth if needed to achieve the perfect texture.
In a large bowl, combine the beet puree with the remaining broth, yogurt, cucumber, dill, lemon juice, apple cider vinegar, red onion, and garlic. Stir well to incorporate all ingredients.
Season with salt and pepper, tasting as you go to achieve your perfect balance of earthy, tangy, and savory notes.
Cover the bowl and refrigerate for at least 4 hours, preferably overnight. This resting period allows the flavors to meld and deepen.
Before serving, taste the soup again and adjust seasonings if necessary. Ladle into chilled bowls and garnish with your choice of toppings—hard-boiled egg slices, a dollop of sour cream, fresh dill sprigs, or thinly sliced radishes.