Place the flour and baking powder in a medium bowl and whisk to combine.
Combine the butter, sugar, lemon zest and salt in the bowl of an elecric mixer fitted with the paddle attachment, and mix until smooth. Be careful not to over beat. With the mixer on low speed, add the eggs, and then egg yolk, one at a time, scraping down the sides of the bowl as necessary, and mix until well combined. Stir in the flour mixture and mix until the dough is smooth, 1 minute. Cover the bowl with plastic wrap and refrigerate for at least 1 hour or up to 3 days. The dough will keep in an airtight container, or portioned out in zipper-lock bags, in the freezer for up to 1 month.
Preheat the oven to 425 degrees. Make the lemon glaze; Combine the confectioners' sugar, lemon juice, and lemon zest in a medium bowl and whisk to dissolve the sugar.
Butter the madeleine or muffin pans and flour them. (If you are using nonstick pans, there is no need to butter and flour them). Spoon the batter into the pans until each cup is about 3/4 full. Bake until risen and golden, about 8 minutes. Remove the pan(s) from the oven, immediately turn the madeleines out of the pans, and brush them with the lemon glaze if desired. Madeleines are best eaten on the day they are baked.