Put water, dried bouillon, spices, and mushrooms in a saucepan and bring to a low boil. After boiling begins, turn the heat down to low simmer.
Place 1/4 cup of milk in microwave on medium and heat until small bubbles begin to form. (Use microwave safe container, time will depend on microwave wattage.).
While bouillon mixture and milk are heating, put beef tallow and butter in medium pot, 4 quart, and turn heat to medium high. When bubbling starts, begin whisking and add flour. Continue whisking until the roux is dark brown. NOTE: Because beef tallow has a high smoke point - 450 degrees - a dark brown roux can be achieved in about 5 minutes.
Strain the bouillon mixture and place next to the roux along with the hot milk. NOTE: While performing this step, turn off the heat under the roux so that it won't burn.
Turn the heat under the roux back to medium high and begin whisking while slowly adding the bouillon. Continue whisking and add the hot milk. Bring to low boil for two minutes, while continuing to whisk.
Remove the roux from heat and mix a water/cornstarch slurry. Whisk the slurry into the roux. NOTE: The slurry can be prepared in advance.
Taste and adjust spices as necessary. Serve or store in refrigerator or freezer.