How it works:
• Combine carrots, celery, and twice as much onions in a large pan.
• Throw in some thyme, parsley, dried mushrooms, a bay leaf, garlic, and a dollop of tomato paste.
• Cook it all down over medium-high heat until it's almost jamlike and deeply caramelized, about 15-20 minutes, with an occasional stir.
• Sprinkle some flour over it all, and caramelize it as you would a roux.
• Stir in some water and bring it up to a simmer.
• Let it simmer for 20-25 minutes until it's nicely thickened.
• Strain the mixture with a fine strainer, pushing down on the solids to extract all the flavor.
• Stir in some cold, diced butter to smooth out the flavors.
• Add a splash of port, sherry, or red wine vinegar to balance the long-cooked flavors.