In a saucepan over medium heat, melt ¼ cup of the butter. Add the flour and cook for 1 minute, stirring constantly. Add the raspberry purée and bring to a boil, stirring with a whisk. Simmer over low heat for about 1 minute or until it thickens.
Pour into a large bowl, cover with plastic wrap directly on the surface to prevent the formation of a skin and cool to room temperature.
Add the sugar and the remaining butter (1 ¼ cups). With an electric mixer, beat at medium-high speed for
about 5 minutes or until the frosting is smooth and creamy (see note).
The raspberry frosting keeps for up to 3 days at room temperature or in the refrigerator. If refrigerated, let warm to room temperature and beat again to restore its creaminess.
The sugar will take about five minutes to dissolve into the cream. Although the texture may seem right sooner, beat for a full five minutes for best results.