Place strawberries in the bowl of a small food processor; process until pureed. In the bowl of an electric mixer fitted with the paddle attachment, beat together butter and salt on medium speed until light and fluffy. Reduce mixer speed and slowly add confectioners' sugar; beat until well combined. Add vanilla and 3 tablespoons strawberry puree (save any remaining strawberry puree for another use); mix until just blended. Do not overmix or frosting will incorporate too much air. Frosting consistency should be dense and creamy, like ice cream.