Using a stand mixer with the paddle attachment (or electric mixer), beat the butter and sugar until fluffy. Add the vanilla extract and orange zest, and keep beating while adding the 4 eggs plus 2 egg yolks, one at a time.

In a mixing bowl, whisk together the flour, baking powder, and salt. Whisk together the orange juice and baking soda in a separate bowl or measuring cup. With the mixer on low, add the flour mixture to the butter mixture, one cup at a time, alternating with orange juice and milk. Beat until well combined.

Check the dough, and if it's too sticky, add 0.25 to 0.5 cup more flour.

Cover the dough with a clean towel or cling wrap and let rest at room temperature for 30 minutes.

Preheat the oven to 400°F. Line 2 large baking sheets with parchment paper.

Form the dough into golf ball-sized rounds. Roll each round out into about 8-inch ropes. Fold it in a U-shape and twist the arms to form a braid, pressing the ends together at the end. Transfer the cookies to the baking sheets. Continue until all of the cookies are formed.

To make the egg wash, combine the egg yolks with water and whisk until completely combined. Brush each cookie with the egg wash.

Bake the cookies for 20 to 30 minutes, or until they are golden brown. Halfway through baking, rotate the trays by placing the bottom baking sheet on top and the top baking sheet on the bottom.

Remove from the oven and let the butter cookies cool completely before serving or storing.