Preheat the oven to 375°F (190°C). Generously brush a madeleine pan with Butter and dust it with Flour, tapping out any excess.
Melt the Unsalted Butter in a small saucepan or microwave, then set aside to cool slightly.
In a large bowl, whisk the Eggs and Granulated Sugar together until the mixture is pale, thick and slightly ribbon-like, about 5–7 minutes with a hand or stand mixer.
Stir in the Vanilla Extract and the Lemon Zest until evenly distributed.
Sift together the All-Purpose Flour, Baking Powder and Fine Salt over the egg mixture and fold gently with a spatula until just combined — do not overmix.
Fold the cooled melted butter into the batter in two additions, gently incorporating until smooth and cohesive.
Cover the batter and chill it in the refrigerator for at least 30 minutes (this helps create the characteristic hump), or up to a few hours.
Spoon or pipe the chilled batter into the prepared madeleine pan, filling each mold about three-quarters full. Bake at 375°F (190°C) for 8–12 minutes, until the edges are golden and the centers spring back when touched.
Let the madeleines cool in the pan for 1–2 minutes, then carefully unmold onto a wire rack to cool slightly.
When cool or just warm, dust the madeleines with Powdered Sugar and serve.
