In a large mixing bowl, combine the flour, granulated sugar, salt, and instant yeast. Mix well to combine.
In a separate bowl, whisk together the warmed milk, melted butter, egg, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and mix until a dough forms. Knead the dough on a floured surface for about 5-7 minutes until it is smooth and elastic.
Place the dough in a greased bowl, cover with a kitchen towel, and let it rise in a warm place for about 1 hour, or until it has doubled in size.
Preheat your oven to 350°F (175°C).
Once the dough has risen, roll it out on a floured surface into a rectangle about 1/4 inch thick.
Sprinkle the cocoa powder evenly over the dough, then add the chocolate chips on top.
Starting from one long side, roll the dough tightly into a log. Pinch the seams to seal.
Cut the log in half lengthwise to create two long pieces. Twist the two pieces together, keeping the cut side facing up.
Place the twisted dough into a greased loaf pan. Cover and let it rise for another 30 minutes.
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and a toothpick inserted comes out clean.
Allow the babka to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely. Dust with powdered sugar before serving.