Using a stand mixer with the paddle attachment, beat the butter and sugar until fluffy. Add vanilla extract and orange zest, then slowly add eggs and egg yolks one at a time.

In a mixing bowl, whisk together the flour, baking powder, and salt. In a separate bowl, combine orange juice and baking soda. Gradually add the dry ingredients to the wet mixture, alternating with milk and orange juice, mixing until just combined.

Check the dough consistency; add more flour if it's too sticky. Cover and let rest at room temperature for 30 minutes.

Preheat oven to 400°F. Line baking sheets with parchment paper.

Divide dough into golf ball-sized portions. Roll each into about 8-inch ropes, form into U-shapes, braid, and seal ends. Place on prepared baking sheets.

Prepare egg wash by whisking egg yolks with water. Brush atop each cookie.

Bake for 20-30 minutes until golden brown. Rotate trays halfway through.

Cool cookies on wire racks before serving.