This is a classic French sauce from Julia Child's cookbook Mastering the Art of French Cooking. If you don't have two hours to spend making it, skip straight ahead to the Quick Vegan Brown Sauce.
For about 1 quart of Brown Sauce you will need
A heavy-bottomed 2qt saucepan
A wooden spatula or spoon
A wire whip
1/3 cup each: diced celery, carrots, onions
4 T olive or canola oil (reduced from original recipe)
4 T flour
6 cups boiling mushroom stock
2 T tomato paste
A medium herb bouquet: 3 parsley sprigs, 1/2 bay leaf, 1/4 tsp thyme tied in cheesecloth
Cook the vegetables slowly in the oil for about 10 minutes.
Blend the flour into the vegetables, stirring constantly over moderately low heat 8-10 minutes or until the flour turns a golden brown. (This is a vegan roux.)
Remove from heat. With a wire whip or whisk, immediately blend in all the boiling liquid at once. Add the herb bouquet.
Simmer slowly, partially covered, for 2 hours or more. Add more liquid if the sauce thickens too much.