In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy. Add the eggs, one at a time, mixing well after each addition.
Stir in the vanilla extract and lemon or orange zest, if using.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms. The dough should be slightly sticky but manageable.
Shape the dough into a disk, wrap it in plastic wrap, and refrigerate for about 30 minutes. Chilling the dough will make it easier to handle.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
On a floured surface, roll out the chilled dough to about 1/4 inch thickness. Use cookie cutters to cut out shapes from the dough. Traditional Areias cookies are often round or flower-shaped.
Place the cut-out cookies on the prepared baking sheet, leaving some space between them.
Bake the cookies in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Remove the cookies from the oven and let them cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.