prepare the ingredients
Melt the butter in a saucepan over medium heat. Add grated orange zest and set aside. Mix the roasted hazelnuts and sugar in a chopper or food processor to get a fine texture. Sift the mixture into a small bowl. Separately sift the flour, baking powder, and salt into the bowl with the hazelnuts.
Add eggs, sugar, and vanilla to a large bowl. Mix for 6 - 8 minutes with an electric mixer or until the mixture is pale and tripled in size. Then, using a spatula, stir in the dry ingredients making sure the mixture is smooth and airy. Gently stir in the (cooled) orange-flavored butter.
rest the madeleine batter
Place the madeleine batter in a fridge for 30 minutes to 2 hours. Place a rack in the middle of the oven and preheat it to 200 °C / 390 °F. Grease the madeleine pan with butter using a brush or with cooking spray. Sprinkle with flour and shake off any excess. Spoon one tablespoon of batter into the center of each scalloped well filling it approximately two-thirds.
bake and serve
Transfer the Hazelnut Orange Madeleines to a preheated oven and bake for 6 - 8 minutes at 200 °C / 390 °F. Transfer the baked Madeleines to a rack, then arrange them on a plate. Optionally sprinkle with icing sugar.