1.) In a microwave safe measuring cup, heat the milk for 30 seconds at a time until warmed throughout, about 2-3 times. In the bowl of a stand mixer add the envelope of active dry yeast and the sugar. Pour the warmed milk on top and whisk lightly. Let it sit for 10 mins until frothy.
2.) Add in the egg, egg yolk, and sugar and whisk lightly. With the mixer running on low using the dough hook attachment, add the flour in slowly working your way up to medium speed as you finish adding it in. Add in the salt and continue to mix for 3 mins.
3.) Cut the butter into small pieces and add it to the mixer. Continue mixing for 3-5 more minutes until the mixture is completely combined. You may have to stop and scrape the butter down into the dough to get it to mix in. The dough will be a little bit sticky.
4) Pour the dough onto a lightly floured surface and knead by hand adding up to an additional ½ tsp flour until it is no longer sticky. Place the dough back in the bowl and cover it with a tea towel. Place it in a warm area (such as your stop top with your oven on below) for 1 hour until it is doubled in size.
5.) Right before rolling out the dough, place the white chocolate chips and oil in a small microwavable safe bowl and microwave 30 seconds at a time until melted, mixing in between.
6.) Pour out the dough onto a floured surface and roll into a 12×16” rectangle. Spread the white chocolate all over the dough leaving a 1” border. Roll the dough into a log, then using a sharp knife, cut down the center of the log vertically so you have two strands. Twist the strands together, and pinch the ends together.
7.) Place the babka in a 9×5” parchment lined loaf pan and let it rise again for 30 mins.
8.) Preheat the oven to 350° F and bake the babka for 40-45 mins until the top is golden brown and puffed up.
9.) While the babka is baking, make the simple syrup. Combine the sugar and water in a small saucepan and bring to a bowl. Stir until sugar has fully dissolved then take off the heat. Melt the last remaining chocolate chips in the microwave and set aside.
10.) When the babka comes out of the oven brush with the simple syrup (this makes it super shiny on top) and drizzle with the white chocolate.