Puree strawberries in a blender or food processor or using the chopper attachment of an immersion blender. Measure out 1/4 cup of pureed strawberries and add to a small pot. Discard the rest.
Add granulated sugar to the pot and bring to a simmer over medium heat. Cook, stirring frequently, until reduced to 1 1/2 to 2 tablespoons, 2 to 3 minutes. Remove from heat. Cool on the counter until completely cool to the touch, stirring occasionally to speed up the process.
In a medium bowl, beat softened butter until light and fluffy. Add powdered sugar, 1 teaspoon of completely cooled puree, vanilla extract, and salt. Beat for 30 seconds.
Add 2 more teaspoons of the puree, one at a time, beating well after each. After the final teaspoon, continue to beat until the frosting is light and fluffy. Discard remaining cooked puree.*
Use strawberry frosting over cookies, cupcakes, or brownies, and enjoy! Frosting will be softer than regular buttercream, but will firm up in the refrigerator.