In a small bowl, mix together 1/2 cup (113g) of the melted butter with the lemon zest and vanilla extract. Set aside.
In a medium bowl, whisk together the flour, baking powder and salt. Set aside
In a large bowl, beat the eggs and granulated sugar, with an electric mixer at medium-high speed, to ribbon stage, about 8 minutes. The batter should look thick, voluminous and light in color.
Sift the flour mixture into the egg mixture in 2 additions, gently folding it in just until combined.
Gently fold the butter mixture into the batter in 3 additions. Cover and refrigerate the batter for 30-45 minutes.
Meanwhile, preheat the oven to 350ºF (180ºC). Brush the molds of a heart-shaped madeleine pan* with melted butter, making sure to get butter into all of the crevices.
Scoop about a generous tablespoon of batter into each of the molds. Bake until the tops are puffed and springy and the edges start to turn light golden brown, about 8-10 minutes. Transfer the madeleines to a cooling rack.
To make the icing, whisk the powdered sugar together with 1 tablespoon of melted butter and 2 tablespoons of puréed strawberries in a medium bowl. Add more of the puréed strawberries until your desired consistency is achieved.
Brush the scalloped side of the cooled madeleines with the strawberry icing, using a small pastry brush. (Alternately, you can thin the icing with a bit of milk and dunk one side fo the madeleines into the icing.
To find the heart-shaped madeleine pan I used, click here.