In a medium-sized bowl, whisk together the all purpose flour, cake flour, cocoa powder, baking powder and salt until well blended.

In a large bowl, beat the butter and sugar together, with an electric mixer at medium speed, until light and fluffy. Beat in the eggs and vanilla extract in 3 separate additions, making sure each one is incorporated before adding the next. On low speed, or by hand, stir in the flour mixture just until combined. Refrigerate the dough just until it's easier to work with, about 10-15 minutes.

Meanwhile, preheat the oven to 350ºF. (180ºC). Line 2 large cookie sheets with parchment paper.

Divide the cookie dough into 24 portions, about 2 tablespoons (35g) each. (I used a #30 portion scoop.**) Roll them into 1 1/2-inch balls. Place the cookie dough balls onto the baking sheets about 3 inches apart. Bake until the cookies are puffed and start to darken around the edges, about 9-11 minutes. Do not over bake. Let the cookies cool on the baking sheet for 1 minute, then transfer them to a cooling rack.

In a small saucepan over low heat, whisk together the maple syrup, water, and cocoa powder until smooth. Remove from heat and set aside to cool to room temperature.

Melt the chocolate in a medium-sized bowl set over a pan of barely simmering water, making sure the water doesn't touch the bottom of the bowl. Stir gently until smooth. Remove from heat and set aside to cool to lukewarm.

In a large bowl, beat the butter, with an electric mixer at medium speed, until smooth and pale. Add the powdered sugar and salt and continue beating until smooth and well blended.

Gradually add the cooled maple syrup mixture and beat on low speed until combined. Stir in the melted chocolate until well combined. Smooth out any air bubbles by stirring gently with a rubber spatula.

Frost the cooled cookies. Top with sprinkles if desired.