Process 2 pints strawberries in a food mill, discarding excess pulp and seeds.
Combine the processed strawberries, 1 3/4 cups powdered sugar, and sour cream in a Dutch oven; beat well with a wire whisk. Gradually add wine and water, beating until mixture is well blended.
Cook over low heat, stirring constantly, until thoroughly heated and slightly thickened. (Do not boil.) Remove from heat; cool to room temperature. Cover and chill thoroughly.
Serve soup in chilled dessert bowls. Garnish each serving with a strawberry, and sprinkle with additional powdered sugar.