Cook strawberry puree in a pot over medium heat until it reduces to 1/4 cup, about 25 minutes. Remove from heat and allow to cool.

In the bowl of a stand mixer with paddle attachment, cream together butter and 3 1/2 cups powdered sugar until light and fluffy. Beat in vanilla. Beat in cooled strawberries and continue beating until frosting becomes thick and spreadable. If too soft, add remaining 1/2 cup powdered sugar.

Use to frost cakes, cupcakes and other desserts.