Peel the beets and grate them on the large holes of a box grater. Set aside.

In a 4-quart / 3.8L saucepan, combine the grated beets and vegetable broth. Bring to a boil over medium-high heat, then reduce to a simmer.

Simmer for 20 to 25 minutes, until the beets are fork tender.

Stir in the vinegar, sugar, salt, and pepper while the broth is still warm, since the vinegar helps the color stay bright pink. Taste and adjust the salt.

Remove from heat and cool at room temperature for 15 minutes, then transfer to the fridge. Chill completely, at least 2 hours or overnight.

Once fully cold, whisk in the buttermilk and lemon juice until the broth turns bright pink and smooth.

Stir in the diced cucumber, radishes, and green onions. Fold in most of the dill, saving some for garnish.

Ladle into bowls. Top each with chopped hard boiled egg, a dollop of sour cream, and the reserved dill.