Cut the brioche bread into cubes and set aside.
In a bowl, combine 4 eggs and 3/4 cup sugar.
Heat 4 cups of heavy cream in a saucepan just until it comes to a slight simmer (not a boil). The slowly put the hot cream into the egg and sugar mixture making sure to stir constantly.
Add the cinnamon and vanilla and stir lightly just to incorporate.
In a large bowl add the cubed bread, golden raisins, and chopped pecans. Then pour the warm cream and sugar mixture into the bowl. Gently stir with a spatula.
Butter a 9×13 inch baking pan and pour the bread pudding into it. Bake at 360 degrees Fahrenheit for 35-40 minutes.
Meanwhile combine the cornstarch and 1/2 cup sugar and set aside.
Melt 3 tbsp of butter in a small saucepan, then add 2 cups of heavy cream, and the sugar and cornstarch mixture. Stir or low heat until it begins to thicken.
Remove from heat and add the 1 tsp vanilla and 1 tbsp rum.
Once the bread pudding is baked, pour the sauce over the top.