Preheat oven to 350° F. Spray Madeleiine pan with non-stick baking spray. Set aside.
Measure 1/4 cup of the eggs into a bowl, reserving the rest for a later addition. Add the flour and sugar; beat on high until a thick paste forms. Let rest for 10 minutes. (See Tip 1)
Meanwhile, melt the butter in a saucepan over medium heat; bring to a boil, and let the butter brown lightly, about 10 minutes. Place the pan in a ice water bath until the butter is cool, but still liquid.
Add the remaining egg, lemon zest, lemon juice, vanilla extract, salt and butter to the batter. Beat until thoroughly blended., about 1 minute.
Place a generous tablespoon of batter into each of the Madeleine cups. (See Tip 2)
Bake at 350° F for 14 to 15 minutes, or until cakes are lightly browned around the edges, humped in the middle and slightly shrunk from the cups. Unmold onto a wire rack to cool completely.
When cool, turn the shell side up and dust with confectioners sugar if desired. Yield: 1 1/2 dozen.