Melt 5 tablespoons of butter and set aside to slightly cool as you prepare the rest of the batter.
In a small bowl, mix sugar and cornstarch. Set aside.
Using an electric mixer or a stand mixer with the whisk attachment, beat the aquafaba on medium-high speed until it becomes foamy and opaque. Continue beating until reach medium peaks, about 3 – 5 minutes.
With the mixer on high, gradually add sugar mixture, about 1 teaspoon at a time, or sprinkle it in slow as slow can be, mixing after each addition, until sugar is dissolved (about 15-20 seconds between each addition).
Beat in the lemon zest and vanilla extract until combined. Note: The remaining ingredients are mixed by hand; you no longer need the mixer.
Place a fine-mesh strainer over the bowl and stiff the flour and baking powder into the bowl. Then, gently fold into the aquafaba mixture using a spatula or wooden spoon.
Stir in half of the cooled melted butter until fully incorporated. Then stir in the rest of the butter and gently incorporate.
Cover the batter with plastic wrap, pressing it directly onto the surface of the batter. Chill in the refrigerator for 60 minutes.
Melt the extra 2 tablespoons of butter. Using a pastry brush, brush the pan with melted butter. Refrigerate the pans until the butter hardens.
Preheat the oven to 350°F (180°C).
Spoon 1 generous tablespoon of batter into the center of each scallop-shaped well (you can use an ice cream scoop). No need to spread it to the edges. Just plop it in the center.
Bake for 10-12 minutes, or until the edges are golden brown and the centers spring back after being lightly pressed with your finger. Invert the pan onto the counter. Transfer the warm madeleines to a wire rack to cool slightly. Note: Do not overbake these cookies, or they will be dry.
Serve with a light dusting of confectioners’ sugar, if desired.