Preheat your oven to 350°F (175°C).
In a large bowl, whisk together milk, molasses, brown sugar, and melted butter until fully combined.
Add in the eggs, one at a time, whisking continuously until smooth.
In a separate bowl, whisk together flour, ginger, cinnamon, baking powder, and salt.
Gradually add the dry mixture to the wet ingredients, stirring until combined, but do not overmix.
Pour the mixture into a greased baking dish.
Bake in the preheated oven for 30-35 minutes or until a toothpick comes out clean.
While the pudding bakes, prepare the vanilla sauce by heating the cream in a saucepan over medium heat.
Add sugar and vanilla, whisking until the sugar has dissolved.
Allow the sauce to simmer gently for a few minutes until slightly thickened.
Once the pudding is done, let it cool slightly before serving with the warm vanilla sauce.