Preheat the oven to 175 degrees circulating air or bottom heat. Butter the baking pan lightly.
Whisk the eggs with the milk and vanilla extract. In another bowl, combine flour, ground pistachios, grated coconut, sugar, baking powder and salt.
Add the softened butter, piece by piece, to the dry ingredients and work into the mixture with your fingers until it resembles small peas. Using a food processor, hand mixer or spatula, stir in the egg and milk mixture. Divide the batter evenly over the prepared baking pan.
Bake the cake for 23 to 25 minutes. Prick the center with a toothpick to check. If it comes out clean, the floors are done. Leave to cool in the mold for 10 minutes, then remove and let cool completely on a wire rack.
Place the powdered sugar on the plates and arrange the cake on the plate. Turn out the panna cotta.