Stir together cornstarch and 3/4 cup sugar in a large saucepan. Add frozen berries, lemon juice, and vanilla, and bring to a boil, stirring constantly; boil 1 minute. Pour into a lightly greased 2-quart baking dish.
Combine baking mix and 2 tablespoons sugar. Cut in softened butter with a fork or pastry blender until mixture is crumbly; stir in egg and milk. Drop by 2 tablespoonfuls onto hot berry mixture.
Bake at 400° for 20 to 25 minutes or until cobbler is golden and bubbly. Serve warm with vanilla ice cream or sweetened whipped cream, if desired.