Preheat your oven to 375°F (190°C). Grease and flour your Madeleine molds or use a non-stick Madeleine pan.
In a small saucepan, melt the butter over low heat. Once melted, remove from heat and let it cool to room temperature.
In a mixing bowl, sift together the flour, baking powder, and salt. Set aside.
In another bowl, using an electric mixer, beat the eggs, granulated sugar, and vanilla extract together until the mixture is pale and fluffy. This usually takes about 5 minutes.
Add the Kabocha and mix for another 2 minutes
Gently fold the sifted dry ingredients into the egg mixture in two or three additions. Be careful not to overmix; just fold until the ingredients are combined.
Pour the melted and cooled butter over the batter and fold it in until well combined. If you're using lemon zest, add it at this stage and fold it in as well.
Cover the batter and refrigerate it for at least 30 minutes. Chilling the batter helps the Madeleines achieve their distinctive hump.
Spoon the batter into the prepared Madeleine molds, filling each about 3/4 full.
Bake in the preheated oven for 10-12 minutes or until the edges are golden brown and the centers spring back when lightly touched.
Remove the Madeleines from the oven and let them cool in the pan for a few minutes. Then, transfer them to a wire rack to cool completely.
Optional: Dust the cooled Madeleines with powdered sugar before serving.
Enjoy your homemade French Madeleines with a cup of tea or coffee!