Add in strawberry puree, vanilla extract and jam. Beat with an electric mixer until well combined. If a thicker frosting is desired, add more powdered sugar, 1/4 cup at a time. If a thinner frosting is desired, add in more strawberry puree, milk or cream, one tablespoon at a time, mixing well, until desired consistency is reached. Frost cupcakes with an offset spatula or by piping on. Top each cupcake with a fresh strawberry if desired.