Slowly add your flour mixture in thirds alternating with the milk, mixing to incorporate with each addition. Beat until just combined, don't overmix. Divide your batter evenly into your prepared cupcake pan, filling about 2/3 full.
Bring your puree to a simmer over medium-low heat. While stirring frequently, let it simmer until it reduces to half the volume (15-30 minutes). Set aside to cool completely while preparing the rest of the frosting.