Make the babka dough. Heat the milk in the microwave until it reaches 100 degrees F, about 30 seconds. Add the yeast and 1 teaspoon sugar and let sit for 5 minutes or until the mixture is foamy.
Combine the yeast mixture with the all-purpose flour, ¼ cup sugar, salt, vanilla, 2 eggs, and 2 yolks. Mix until the dough comes and knead for 2-3 minutes or until firm. Add the butter a little at a time, mixing well between each addition. Continue to knead the dough until smooth, about 7-8 minutes.
Transfer the dough to a clean bowl, cover, and let proof in a warm area for 1 hour. It may not double in size.
Meanwhile, make the filling. In a food processor, pulse together the pistachios, hazelnuts, vanilla, rosewater, salt, and zest of 1 orange until the nuts are coarsely chopped. In a separate bowl, combine the sugar with cinnamon, cardamom, and nutmeg.
Grease a tube pan and set it aside.
Punch down the dough. Lightly dust a clean work counter with flour and roll out the dough until it's a 12x24 inch rectangle. Brush the dough with ⅓ cup melted butter, leaving a ½ inch border.
Sprinkle the spiced sugar evenly on the buttered portion of the dough. Top with the chopped nut filling. Starting with the long side facing you, roll the dough into a tight rope. You should end up with a 24-inch long rope.
Trim the ends of the log and cut it in half lengthwise. Flip the logs so that the cut sides are facing up. Gently pinch the ends of the top of the log together and start to twist the two logs together. Lift one side over the next to form a twist, keeping the cut sides facing up. Transfer the log to the prepared pan, shaping it into a circle. Tuck the ends together to enclose the circle. Sprinkle any of the nuts that may have fallen off on top. Cover the pan and let rise in a warm place for 45 minutes.
Meanwhile, make the honey syrup. Combine the honey with the water and bring to a boil over medium heat. Lower the heat to low and continue to simmer the syrup for 5 minutes. Remove from heat and let cool.
Preheat the oven to 350 degrees.
Bake the babka for 30-40 minutes or until golden brown. Remove from heat and pour the honey syrup on top. Let cool completely.