Preheat oven to 190C/375F.
Grate the zest of one orange and squeeze the juice into a bowl.
Place the sugar and the orange zest in the mixer bowl. Rub the orange zest and the sugar with your fingers until the sugar absorbs the essential oil of the orange zest. It will become orange in colour and will have a fantastic orange scent.
Cut the soft butter into small pieces. Add it to the bowl with the sugar and whisk with the paddle attachment on your mixer for 2-3 minutes at low speed. Scrape the walls of the mixer dish with a spatula and continue whisking the butter and the sugar for another 2-3 minutes until the mixture becomes pale and fluffy.
Separate the yolk from one of the eggs and place it in a small bowl to make the yolk wash with it. Add the two eggs and the leftover egg white to the bowl with the butter mixture. Whisk with your mixer at low speed until the ingredients are combined and the mixture is light in texture.
Add the milk, orange juice, vanilla and brandy or ouzo. Continue whisking until the liquids are blended and the mixture curdles.
Stir the flour and the baking powder to combine.
Gradually add 3 1/2 cups of flour to the mixer bowl while mixing the mixture at low speed. You will see a sticky dough forming. Replace the attachment on your mixer with the kneading attachment and continue kneading the dough with it. Add small quantities of flour and knead until the dough is no longer sticking to the walls of the mixer bowl. Take the silky dough out of the mixer bowl and knead it by hand for a few minutes to ensure it has the right consistency. The dough must be soft, elastic and light.
Use a scale and cut the dough into 25g pieces, or use an ice cream scoop to portion the dough. Roll the piece of dough between your palms to shape into a ball, then pull and roll the ball into a long rope. Cut 1/3 off the dough rope, place the longer piece horizontally on your working surface, and position the top end of the shorter dough piece in the middle of the long horizontal dough rope to touch. Take the left end of the horizontal dough rope and pull it over the top of the vertical rope. Then, place the right end of the horizontal dough rope on top of the folded dough pieces to form a braid. Continue to weave the dough until the braid is completed. Place the ready dough braids on a lined baking tray about an inch apart to allow room for them to rise.
Prepare a yolk wash and brush the braids with it. Sprinkle sesame seeds on top.
Bake the cookies in the middle of the oven for 15 minutes or until they are golden in colour. Take the sheet with the cookies out of the oven and let them cool for a few minutes, then transfer the cookies to a baking grid. Leave the cookies on the baking grid until they are completely cool.
Store Koulourakia cookies in an airtight container at room temperature and consume them within two weeks. You can also store koulourakia in the freezer.