Make the dough: Sprinkle the yeast over the milk in a liquid measuring cup. Add a pinch of sugar, stir and set aside until bubbly, about 7 minutes. 

Add the flour, the remaining ⅓ cup of sugar, eggs, vanilla extract, salt, nutmeg, lemon zest, and the milk and yeast mixture into a large bowl or into the bowl of a stand mixer fitted with the dough hook attachment. Knead the mixture until a dough comes together, about 5 minutes. If using a stand mixer, mix the dough on medium speed until the dough comes together, about 3 to 5 minutes.

Knead the butter, by hand or with the stand mixer on medium speed, into the dough in three additions, mixing each addition completely before adding more butter. (The dough will initially start to tear and lose elasticity when the butter is added; dust the dough with a bit of flour if it's too sticky.)

Transfer the dough to a large bowl; cover with plastic wrap and let rise at room temperature until doubled in size, about 1½ hours. Punch down the dough, re-cover with plastic wrap, and let it rise in the fridge overnight. 

Make the filling: Place the bittersweet chocolate chips, butter, and vanilla in a medium heat-proof bowl. Heat the heavy cream, sugar, and salt in a small nonstick saucepan over high heat, mixing often, until it just starts to boil, about 5 minutes. Pour the cream mixture over the chocolate chips and butter and whisk until the chocolate mixture is smooth and shiny. Let cool to room temperature. 

Make the topping: Whisk the flour, sugar, cocoa powder, and salt in a small bowl. Smash and work the butter in with your fingers until the mixture is sandy and chunky. Mix in the mini chocolate chips and set aside in a cool place. 

Form the loaves: Coat two 9-inch by 5-inch loaf pans with cooking spray and line with parchment paper, then spray the parchment with cooking spray. Set aside.

Turn out the risen dough onto a lightly floured surface. Cut the dough in half with a bench scraper or chef's knife. Using a rolling pin, roll each half into a 12-inch by 16-inch rectangle on a lightly floured surface. Using an offset spatula, spread half of the chocolate filling over each dough rectangle, all the way to the edges. 

Starting from a long side of the dough, tightly roll each rectangle into a log. Wrap each log in plastic wrap and refrigerate for 15 minutes. 

Unwrap the logs and gently cut each in half lengthwise with a bench scraper or chef's knife. Twist the halves together a few times, starting from the middle. Place each dough twist snugly into each prepared pan, tucking the ends under as needed. Cover with plastic wrap and let rise 1½ hours at room temperature. 

Finish and bake the babka: Preheat the oven to 350°F. Brush each loaf with melted butter and sprinkle with the streusel topping. Bake until puffed and browned, about 45 minutes. 

Meanwhile, make the simple syrup: Combine the sugar and water in a small saucepan. Bring to a boil over high heat, stirring until the sugar dissolves, about 5 minutes. Let cool completely. 

Remove the loaves from the oven and immediately pour ½ cup of simple syrup evenly over each loaf. 

Let the loaves sit for 10 minutes, then remove the babka from the pans, remove the parchment, and let the loaves cool completely on a wire rack. 

Serve the babka at room temperature.