Place the yeast, water, and 1 teaspoon of the granulated sugar in a small bowl. Gently stir so that the sugar does not settle on the bottom of the bowl. Wait about 5-10 minutes for the yeast to activate (you should see the mixture foam up).
Add the flour, salt, and remaining 3 tablespoons of sugar to the bowl of a stand mixer and stir to combine. Pour in the yeast mixture, along with the non-dairy milk and vanilla extract. Attach the dough hook and mix until a rough dough forms, scraping down the sides as needed.
Add the butter and knead on low until it is fully incorporated into the dough; the dough will form a ball and pull away from the sides of the bowl. If the dough looks very wet, you can add more flour, one tablespoon at a time (do not overdo it; your dough should remain soft and slightly tacky). Increase the speed of the mixer to low-medium and continue kneading until the dough appears smooth and elastic, about 8 minutes.
Place the dough in a lightly oiled bowl, cover with a damp tea towel, and allow it to rise in a warm spot (between 70°-80°F) for about 1 ½ hours, until well risen (the dough may not quite double in size; this is okay).
Place the dough in the fridge while you prepare the filling. Add the sugar, cinnamon, cocoa powder, and salt to a bowl and whisk to combine. Add the melted non-dairy butter and 2 tablespoons of the non-dairy milk to the dry ingredients and whisk until fully combined. The filling should be thick but easily spreadable; if needed, add 1 more tablespoon of non-dairy milk. Grease a tube pan with non-dairy butter and sprinkle flour over the whole inside surface of the pan to coat; dump out the excess.
Gently punch down the dough and turn it out onto a lightly floured surface. Using a rolling pin, roll the dough out into a large rectangle; the dough should be about ⅛” thick. Use a spatula to distribute the filling evenly across the dough. If using the non-dairy mini chocolate chips, sprinkle them over the filling.
Starting at the short edge of the dough, begin to tightly roll the dough to create one long log. Using a sharp knife, cut the log in half, so that the layers are exposed. Braid the two halves together, then bring the ends of the braids together to form a circle. Carefully lift the twisted babka dough into the tube pan.
Make the crumb topping: combine the brown sugar, melted non-dairy butter, flour, cinnamon, and salt in a bowl and stir. Use your fingers to distribute the topping evenly over the babka dough.
Cover the pan with a tea towel and allow the dough to rise for about 45 minutes to 1 hour. The shaped babka should rise noticeably, but will not reach the top of the pan.
As the dough finishes rising, preheat the oven to 350°F. Bake for 40-45 minutes, until golden brown. While the babka is baking, make the syrup: combine the sugar and water in a saucepan and heat on the stovetop using medium heat, stirring continuously until the sugar dissolves in the water. Once the mixture simmers, remove it from heat. Brush the syrup onto the baked babka as soon as it comes out of the oven (it will seem like a lot, but keep going).
Allow the babka to rest in the pan for at least 30 minutes, until mostly cool. Gently lift it out of the pan (use a knife or thin spatula to loosen, if needed) and place on a wire rack to cool completely.