To make the cookies, grease two 3 1⁄4 x 1 1⁄2–inch (8.3 x 3.7–cm) nonstick madeleine mold pan and place in the freezer for at least 30 minutes. If your room temperature butter isn’t soft enough to easily smear on a plate, then give it 10 seconds on high in the microwave to give it the correct consistency. Set aside.
In an electric mixer fitted with the whisk attachment, whisk the eggs and sugar on high speed for about 5 minutes, or until pale yellow and thick. Add in the milk, orange zest and vanilla and run the machine on low for 1 minute more.
In a small bowl, whisk together the flour, cornstarch, baking powder and salt. Add the dry ingredients and softened butter to the egg mixture and run the mixer on low for about 40 seconds. Use a rubber spatula to scrape the sides and bottom of the bowl to make sure everything is well blended. The mixture will be smooth and creamy with some small butter bits visible. Cover tightly with plastic wrap and store in the fridge for at least several hours or ideally overnight.
Preheat your oven to 375°F (190°C).
Add 1 tablespoon of batter to each madeleine well. Place the batter in the deep end of each well, not the middle. Do not smooth or flatten.
Bake one tin at a time in the center rack of the oven for 10 minutes. When done, the madeleines will be golden brown around the edges and puffed up in the middle. Let the cookies cool in the tin for 10 minutes before turning out onto a rack. Place some parchment underneath the wire rack.