Step 1: Brown the butter - Place the butter in a heavy saucepan over medium heat and cook, stirring, until the solids turn golden and a nutty aroma develops.

Remove from heat, swirl in the vanilla and lemon zest, and let cool to room temperature.

Step 2: Combine dry ingredients - In a medium bowl, whisk together flour, baking powder, and salt until evenly mixed.

Step 3: Whip eggs and sugar - In a separate bowl, whip the eggs and granulated sugar on medium-high for 3-4 minutes until thick and pale.

Step 4: Fold in dry ingredients - Gently fold the flour mixture into the egg mixture in three additions.

Step 5: Add browned butter - Fold the cooled browned butter into the batter until just incorporated.

Step 6: Chill the batter - Cover the bowl and refrigerate the batter for at least 4 hours, or up to 2 days.

Step 7: Prepare pan and oven - Preheat the oven to 375°F (190°C) and grease the madeleine pan.

Step 8: Fill molds - Spoon batter into each mold, about three-quarters full.

Step 9: Bake until golden and domed - Bake for about 12 minutes until the edges are golden.

Step 10: Cool and finish - Let cool in the pan for 2 minutes, then invert onto a wire rack. Dust with confectioners sugar if desired.