In a large mixing bowl, combine the flour, sugar, salt, and instant yeast. Mix well.
In a separate bowl, whisk together the warm milk, melted butter, egg, and vanilla extract.
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 smooth.
Place the dough in a greased bowl, cover with plastic wrap, and let it rise in a warm place for about 1 hour, or until doubled in size.
While the dough is rising, prepare the filling by mixing the chocolate chips, cocoa powder, sugar, and softened butter in a bowl until well combined.
Once the dough has risen, punch it down and roll it out into a rectangle about 1/4 inch thick.
Spread the chocolate filling evenly over the dough, leaving a small border around the edges.
Roll the dough tightly from one long side to the other, forming a log. Pinch the edges to seal.
Cut the log in half lengthwise to expose the filling. Twist the two halves together and place in a greased loaf pan.
Cover the pan with plastic wrap and let it rise for another 30 minutes.
Preheat the oven to 350°F. Bake the babka for 30-35 minutes or until golden brown.
While the babka is baking, prepare the glaze by combining sugar and water in a small saucepan. Bring to a boil and simmer until the sugar is dissolved.
Once the babka is done baking, remove it from the oven and brush the glaze over the top while it’s still warm. Let it cool in the pan for 10 minutes before transferring to a wire rack to cool completely.