Preheat oven to 325 degrees F. with rack positioned in the center of the oven. In a bowl, sift together flour, baking powder, salt, and set aside. In a mixing bowl with an electric mixer fitted with a paddle (if available), beat butter until soft and fluffy. Gradually add sugar and beat until very light and creamy. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla. Gradually stir in the flour mixture and blend well. Turn the batter into Madeleine pans that have been spread with a generous amount of softened butter and dusted with flour. Use a spatula to scrape the batter into the pans and level off completely. Clean the edges of the pan with a paper towel. Bake in oven for about 10 to 15 minutes or until cake has risen and is golden on top, and a tester inserted in the center comes out clean. Then slide a knife around the sides to loosen. Tip out onto rack right side up. Use a pastry brush and lightly brush the top of each cake with lemon syrup. Allow them to cool and then place madeleines in an air-tight container.
Combine all ingredients in a small saucepan and bring to a boil until sugar dissolves. Remove from the heat and let mixture steep for 20 minutes. Strain syrup to remove herb leaves.