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! In a large mixing bowl, add the melted butter, sugar (both kinds), and mix well until incorporated.
Add the rest of the ingredients: the 2 eggs, orange or lemon zest, baking powder, and flour (3 cups). Knead well until you get a smooth dough. It will be very soft and sticky; you can add about ½ cup more flour, but do resist the urge 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, 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 on a non-stick baking sheet. Slightly beat one egg with a tablespoon of milk and use it to brush the cookies.
Bake at 325-350 °F for 20-25 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 and 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 or 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.