For the pickled strawberry jam: In a blender, puree the strawberries until smooth. In a small saucepan, whisk the sugar with pectin and 1⁄2 teaspoon of the salt. Scrape the strawberry purée into the saucepan along with both vinegars, and stir to combine. Bring to a boil over high heat, and then reduce the heat to medium-low, and cook the jam, stirring, until thickened and glossy, 10 minutes. Remove the jam from the heat and let cool completely. Spoon 5 tablespoons of the jam into a small bowl for the frosting, and refrigerate the remaining jam for up to 2 weeks.
For the pickled strawberry frosting: In the bowl of a stand mixer fitted with the paddle, cream the butter with the confectioners’ sugar on medium-high speed until pale and fluffy, 3 minutes. Meanwhile, in a small bowl, stir the reserved 5 tablespoons pickled strawberry jam with the remaining 1⁄4 teaspoon salt and the citric acid. On low speed, slowly pour in the jam and then beat until smooth and fluffy, 1 minute.