Place the flour in a medium bowl and mix in 1/3 cup of melted ice cream. Using a fork or a hand whisk, whisk the ice cream and flour until smooth.
Continue adding melted ice cream (1/3 cup at a time) to the flour mix until you have incorporated the two together and you have a smooth mix.
Place the mix in a pan over the stove (low heat) and allow it to simmer. Once you notice it starts to simmer, vigorously stir it with a hand whisk until it has thickened and you have a paste like mixture.
Place it in a bowl, cover with a plastic wrap and allow it to cool to room temperature.
In a bowl of a standing mixer fitted with the paddle attachment, place the butter and sugar and mix starting with medium speed and increasing speed to high for about 5 minutes.Scrap the sides and bottom of the bowl.
With the mixer on low, add the ice cream/ flour mix and increase speed too high.
Keep mixer for about 5 extra minutes or until you have a thick and fluffy buttercream.