With a hand mixer or stand mixer fitted with the paddle attachment, beat butter for 2 minutes, until smooth and creamy, scraping down the sides of the bowl and the beater as necessary. Add the powdered sugar, 1/2 a cup at a time, beating until combined. Add puree, vanilla extract, and jam, and beat on medium speed until fully combined, being sure to scrape down the sides of the bowl and beater as needed. If necessary, adjust the consistency by adding more powdered sugar or more strawberry puree, to thicken or thin it out. Place in a piping bag, or use an offset spatula to frost cupcakes (this makes enough frosting to generously frost the cupcakes). Garnish with sliced strawberries, if desired.