Melt the butter and let it cool.
Whisk the eggs with the sugar to make the mixture white, for about 5 minutes.
In a separate bowl, mix the flour, baking powder and salt. You may want to sift the mixture.
Add the cooled melted butter to the sugar and egg mixture and mix in the pistachio paste. Use a wooden spatula to mix the mixture until you get an homogeneous preparation.
Finally, add the dry ingredients gradually, mixing gently and carefully with a wooden spatula, until the mixture is smooth.
Cover and chill in the fridge for 1 to 2 hours.
Then remove from the fridge and leave at room temperature for about 15 minutes.
Meanwhile, preheat the oven to 220°C.
After 15 minutes, grease the moulds (oil or butter) and fill them about 3/4 full with a small spoon or a pastry bag.
Bake at 200°C for 10 minutes. Check the cooking with the tip of a knife and extend the cooking time by 2/3 minutes if necessary.
Remove the madeleines from the tin and leave them to cool on a rack.