Make the dough
Mix the yeast and nondairy milk and a pinch of sugar in a bowl and set aside five minutes until it froths, indicating it's alive.
Place four cups of flour in a large bowl or the bowl of a stand mixer.
Add the salt, 1/3 cup sugar, lemon zest, nutmeg and vanilla and mix well.
Add the yeast mixture and aquafaba and knead on medium speed until the dough comes together in a ball. If the mixture is too sticky, add flour, a tablespoon at a time, until a supple, smooth dough forms.
Add half the vegan butter and knead until it's absorbed by the dough. Repeat with the other half and knead another five to six minutes until you have a very smooth, elastic dough.
Make a ball of the dough and place in an oiled bowl, turning once to coat the top. Cover with plastic wrap and set aside to rise in a warm place for 2 hours.
After two hours, punch the dough down, form into a ball, place into the bowl once more, cover, and place in the refrigerator overnight or at least for six hours to let the flavor develop.
Make the fudge filling:
Place the cashew cream and sugar in a small saucepan. Heat on medium-low heat until the sugar is melted, stirring frequently to ensure it doesn't stick to the bottom. Add the chocolate and the softened butter and stir until very smooth. Turn off the heat and stir in the vanilla and salt. Refrigerate until use, which thickens it up further
Make the streusel:
In a food processor, process the chocolate chips until they break down into smaller pieces. Add the flour, cocoa, salt and butter and pulse 2-3 times until the mixture comes together in large crumbs.
Make the syrup:
In a small saucepan, heat the water and sugar until the sugar is completely dissolved, 2-3 minutes. You need to do this right before the babka comes out of the oven.
Make the babka:
Oil and line with parchment paper two 9-inch loaf pans.
Knead the refrigerated dough briefly and divide into two.
On a floured surface, take one portion of the dough and roll it out evenly into a 18 X 8 inch rectangle.
Take half the fudge filling and using a spatula or a spoon, spread it evenly across the surface of the rectangle.
Using your fingertips, and starting with the long side, roll the dough into a tight coil, the way you would a jelly roll. Seal the ends. Cover with a kitchen towel and place in the freezer for 10 minutes.
Repeat the process with the second piece of dough.
Now take the first coil of dough out of the freezer and cut it lengthwise into half, using a sharp knife to expose the filling.
Braid the two halves and then fold them over once to make them fit into the loaf pan.
Snuggle the dough into the pan. Repeat with the other coil of dough.
Place the loaf pans, covered, in a warm place for 1 to 1 1/2 hours. The dough will rise but will not double. The loaves will rise further in the oven.
Before the loaves go into the oven, scatter the streusel on top.
Preheat the oven to 350 degrees. Bake the loaves for 50 minutes.
Remove the cakes to a rack and immediately poke all over with a skewer, all the way to the bottom. Then pour on the sugar syrup, making sure you divide it evenly between the two cakes.
Remove the loaves from the pan, and continue to cool them on a rack.