Re-hydrate the dried mushrooms in the stock for 15 minutes. Agitate the mushrooms to remove any grit, then remove the mushrooms, chop roughly, strain the stock through cheesecloth and reserve both separately.
Melt the butter in a saucepot, add the shallot, button mushrooms, thyme, and black trumpets and cook for 4-5 minutes, stirring occasionally until the mixture is lightly caramelized. De-glaze the pan with the brandy, then add the chicken stock and reduce the mixture by half.
Transfer the mixture to a highspeed blender and puree, adding a little water or additional stock to help the mixture become smooth. The mixture should be a bit loose to help the blending process, so after it’s finely pureed, transfer it to a saute pan and heat gently, stirring occasionally until it is thick enough to spread into a layer with a spatula on a plate without weeping water, afterwords, taste the mixture for salt and pepper adjust if needed, transfer to a labeled container chill, and reserve until needed.