In a medium bowl, sprinkle yeast over lukewarm milk. Stir to combine, then allow to sit until frothy, about 10 minutes.
In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, orange zest, salt, cinnamon, and nutmeg.
Mix in the frothy yeast with milk, butter, egg, and vanilla extract to bring together the dough.
On a lightly floured surface, knead the dough until smooth and elastic, then knead in the chocolate chips. Transfer to a large, lightly greased bowl. Cover and let rise until doubled 1-2 hours.
Preheat oven 400˚F (200˚C). Line a baking sheet with parchment or lightly grease.
On a lightly floured surface, divide the dough into 15 equal pieces. Form each into a ball and place on the prepared baking sheet about 1/2 inch (1.25 cm) apart. Cover and let rise until puffed, about 30 minutes.
Bake in preheated oven until the tops are golden, 18-20 minutes.
While the hot cross buns are baking, prepare the glaze. In a small saucepan, place the sugar and water over medium heat. Whisk until the sugar is dissolved. Remove from heat and set aside.
Brush the sugar glaze over the hot buns immediately after removing from oven.
Place the melted white chocolate in a pastry bag with a small round tip or small ziploc bag with the corner snipped off. Pipe a cross over each bun.
These hot cross buns are best served warm and within a day of baking.