Add the butter to a large 8qt pot over medium heat. Once it’s melted add in the onions, celery, and carrots, and sauté for 25 to 30 minutes while frequently stirring with a spoon or until well caramelized.
Next, stir in the tomato paste and cook for 8 to 10 minutes to deepen the flavor and loose the raw tomato taste. The color should darken. This is process is known as pince. This lessens the acidic flavor.
Pour in the bone broth or beef stock.
On a square piece of cheesecloth, place to the center the thyme, parsley, peppercorns, and garlic. Fold up the corners and securely tie a double knot around it using butcher’s twine.
Simmer over low to medium heat for 2 hours and be sure to come back every 30 minutes to skim and discard any impurities or fat that collects at the top.
With about 30 minutes left in the simmering process melt the 8oz of butter in a large sauté pan over low to medium heat.
Once melted whisk in the flour until combined. Whisk frequently for the next 20 to 25 minutes to create a dark roux. You should see a visible change in color that is smooth and velvety. A aroma note of nuttiness is also noticed.
At this time slowly pour the roux in the stock pot of stock and veggies while continually whisking until it is incorporated. The stock will immediately thicken.
Cook for a further 20 to 25 minutes.
To confirm doneness. Dip a spoon in the sauce and it should come out completely coated and not runny.