In the bowl of a stand mixer, combine milk and yeast. Stir together by hand and let sit 10 minutes.
Using the paddle attachment, with mixer on medium speed, add sugar, salt, nutmeg, orange zest and eggs.
With mixer on low speed, gradually add 2 3/4 cups flour.
Add butter and vanilla and beat until combined.
Transfer dough to a lightly floured surface. Knead for 5 minutes, adding up to an extra 1/2 cup flour if needed.
Place dough in a large greased bowl, turning to coat the dough. Cover and let rise in a warm place for 1 hour. Dough should double in size.
Punch dough down. Divide into 2 pieces. Shape each piece into a rope about 24 inches long. Place ropes on a parchment paper lined baking sheet. Loosely twist them together, pinching the ends together to seal them.
Separate the dough in 5 places and nest an egg in each hole. Cover and let rise for 1 hour.
Mix together egg and 1 teaspoon milk and brush the dough with it. Bake at 350 degrees for 30 minutes. Cover lightly with foil after 15 minutes to prevent excess browning.
Let cool. Whisk together glaze ingredients and drizzle over bread.Sprinkle with sprinkles.
Notes
If you don't have cane syrup, you can use the maple syrup or double the amount of milk.