Pouding chaude au chocolat ou Fudge a Marie-Thérèse

I feel so much pride in being able to share family recipes. This is from the collection of my maternal Grandmother, Marie-Thérèse Noël-de-Tilly/Lambert. It is in a similar vein as the Québecois dessert Pouding Chômeur (to come to this cooking page, soon) and is singularly bizarre in my mind. With the help of family, I think I've mostly worked out the chemistry behind it. It's best served lukewarm instead of hot, so that the sauce has a chance to thicken, so let it rest at least a half hour before serving. It's equally good cold the next day.

1 cup flour (135g)
½ tsp baking soda (2g)
Pinch of salt (2g)
¾ cup sugar (152g)
2 Tbsps cocoa (11g)
Milk (see instruction #3)
2 Tbsps white vinegar 
2 Tbsps (1oz/28gr) melted butter
1 cup chopped nuts

THE SAUCE
1 cup brown sugar
4 Tbsps cocoa (22g)
OPTIONAL ½ tsp cinnamon
1¾ cups boiling water

1. Preheat the oven to 350°F.
2. In a large bowl combine the flour, baking soda, salt, sugar and cocoa. Make a well in the center.
3. In a half-cup measure, put in 2 Tbsps of white vinegar and fill to the ½ cup mark with milk. Add to the well.
4. Add the melted butter, along with the nuts. 
5. Mix well and place in a greased, square baking dish. Set aside.
6. In a separate bowl combine the brown sugar and second measure of cocoa (optional cinnamon at this point as well). Whisk in the boiling water until perfectly uniform.
7. Pour the sauce over the batter and bake in the oven for about 45 minutes.
8. Serve lukewarm. (my grandmother indicates to serve it hot with the sauce ladled on top. Ultimately, it's your choice.)