1. Mix the raspberries with the sugar and heat, stirring frequently, to a boil. Strain and add more sugar, if desired.
2. Mix the cornstarch with two tablespoons of cooled raspberry juice. Heat the remaining juice to a boil, stir in the cornstarch and cook, stirring, until thickened.
3. Cool and add the lemon juice and cognac. Serve over vanilla ice cream.