Special equipment: a madeleine pan
Adjust the racks to the center of the oven and preheat to 350 degrees F. Butter and flour a madeleine pan.
Add the flour, baking powder, salt and 1/2 teaspoon of the cinnamon to a medium bowl, and whisk to combine.
Add the granulated sugar, vanilla and eggs to the bowl of a stand mixer fitted with the paddle attachment. Beat until the eggs are pale, thick and light yellow, about 5 minutes. Pour in the 4 tablespoons melted butter and mix until just combined. Turn off the mixer and stir in the dry ingredients.
Fill the madeleine pan three-quarters of the way to the top of the molds and bake for 10 to 11 minutes. Cool slightly on a wire rack, 10 minutes, then remove the cookies from the molds.
Combine the confectioners' sugar and remaining 1/2 teaspoon cinnamon in a small bowl. Place the cinnamon sugar in a fine-mesh sieve and dust the cookies before serving.