Melt the butter on low heat and use it while it's still warm. Be careful, as it mustn't be on the hot side! Put it in a large mixing bowl, add the sugar (both kinds), and mix well until incorporated.
Add the rest of the ingredients: the 2 eggs, the orange or lemon zest, the baking powder and flour (750 g). Kneed well until you get a smooth dough. It will be very soft and sticky; you can add about 100 g of more flour but do resist the drive to add any more than that. Instead, bundle up the dough in plastic wrap or wax paper and let it sit in the fridge for 40 minutes.
When the dough is nicely chilled you can use it to form small cookies. There's a bunch of common traditional patterns (“braids”, “snails”, “boats”, “S” shapes, etc.) that are customary in Greece, but you can go for any shape you like! In the meantime make sure you preheat the oven at 375 °F.
Arrange the cookies in a non-stick baking sheet. Slightly beat the extra egg with 1 tablespoon of milk and use it to brush the cookies.
Bake at 325-350 °F for 20 to 25 minutes, until they're golden brown.
If you don't use warm melted butter the brown sugar will not dissolve/incorporate properly. The combination of brown & icing sugar will give you extra crumbly cookies—which is what we're looking for in this recipe. That said, you can use any kind of sugar you like.
Using the warm butter will result in a very soft sticky dough, that will be tough to work with (you will be tempted to keep adding flour to it, only to end up with a stiff dough that will make stiff cookies). Don't skip the chilling part!
You can keep the dough refrigerated (in plastic wrap/wax paper) for up to 1 week, to bake fresh batches at will.
We don't typically frost this type of Easter cookies but you do you! They are best kept in an air-tight container.