Place half of the currant in a large saucepan, cover with water. Bring to a boil, reduce heat and simmer for 15 minutes until the berries are soft. Strain, keeping the decoction. Using an immersion blender, puree the currants.
Mix sugar and cornmeal in a small bowl. Add 3 tbsp. berry puree and mix thoroughly. Put the berry puree and pasta into the pot with the broth and cook over high heat for 5 minutes, whisking. The mixture should thicken.
Reduce the heat, add the remaining currants, lemon and orange juice and zest. Bring to a boil. Remove from heat and cool to room temperature. Add kvass, stir.
Serve on the table, garnished with a spoonful of sour cream and a mint leaf.