Place beets and their juices, 3/4 cup vegetable broth, 1/2 cup sour cream, lemon juice, and sugar into a blender. Blend until smooth; thin with more vegetable broth, if desired. Taste and season with salt as needed.
Transfer borscht to a bowl. Cover and chill at least 3 hours or overnight.
Whisk borscht; spoon 3 to 4 teaspoons into each shooter. Top each shooter with about 1/2 teaspoon of sour cream.
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