1. Combine the canned tomatoes, sugar, peppercorns, bay leaf, and salt in a medium saucepan (2-qt / 2-L capacity). Bring to a simmer over medium heat and cook for 20 minutes, stirring occasionally, until the tomatoes have broken down and the mixture is fragrant and slightly reduced.
2. Press the cooked tomato mixture through a fine-mesh strainer into a bowl, discarding solids. Stir in the brown stock. The combined liquid should be fluid and deeply colored. Set aside, keeping it warm.
3. In a separate heavy saucepan over medium heat, melt the butter and continue cooking, swirling occasionally, until it turns a deep nut-brown color, 3-5 minutes — this is a technique known as browning butter (beurre noisette): the milk solids toast, producing a rich, nutty aroma. Watch closely; it can burn quickly.
4. Add the flour all at once to the browned butter, stirring constantly with a wooden spoon or whisk. Continue cooking the roux over medium heat for 2-4 minutes, until the mixture is uniformly deep brown and smells toasted and nutty — this is a dark roux. It should not smell scorched.
5. Gradually add the warm tomato-stock liquid to the dark roux, whisking or stirring constantly to prevent lumps. Add the liquid in a slow, steady stream, incorporating each addition fully before adding more — this is the technique of tempering a sauce: combining a hot starch base with hot liquid incrementally to achieve a smooth emulsion.
6. Continue stirring over medium heat until the sauce comes to a gentle boil and thickens, 5-8 minutes. The finished sauce should coat the back of a spoon and leave a clean line when a finger is drawn through it. Remove from heat and use immediately, or strain again for a very smooth result.
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