If using pancetta/salt pork, add it to a large, heavy-bottomed stockpot over medium heat. Render until crispy, about 8-10 minutes. Remove the crispy bits (can be used as garnish elsewhere) and leave the rendered fat in the pot. If omitting pancetta, add the olive oil directly to the pot.

Add the diced onion, carrot, and celery (mirepoix) to the pot. Sauté over medium heat, stirring occasionally, until the vegetables are softened and lightly caramelized, about 10-15 minutes. This step is crucial for developing deep flavor.

Stir in the tomato paste and cook for 2-3 minutes, stirring constantly. This process, known as 'pincage', deepens the color and concentrates the flavor of the tomato paste.

In a separate heavy-bottomed saucepan, melt the unsalted butter over medium-low heat.

Gradually whisk in the all-purpose flour, ensuring no lumps. Continue to cook, stirring constantly with a wooden spoon or whisk, for 15-20 minutes until the roux achieves a deep, dark peanut butter color. Be very careful not to burn it, as burnt roux will impart a bitter taste.

Gradually whisk the warm brown stock into the dark roux until smooth and fully incorporated. Bring this mixture to a gentle simmer.

Pour the roux-stock mixture into the stockpot with the cooked mirepoix and tomato paste. Whisk well to combine all ingredients.

Prepare a sachet d'épices by tying the bay leaves, peppercorns, dried thyme, and parsley stems in a small piece of cheesecloth. Add the sachet to the pot (or simply add the spices directly if you don't mind straining them out later).

Bring the sauce to a bare simmer over low heat. Maintain a gentle simmer, not a rolling boil, to prevent clouding and scorching, and to allow flavors to meld slowly.

Simmer for at least 2 to 3 hours, or up to 4 hours, stirring occasionally to prevent sticking to the bottom of the pot.

Throughout the simmering process, use a ladle or spoon to regularly skim any fat and impurities (scum) that rise to the surface. This step is crucial for achieving a clear, clean-tasting sauce.

Once the sauce has cooked sufficiently and reduced to your desired consistency (it should be thick enough to coat the back of a spoon), remove it from the heat.

Carefully remove and discard the sachet d'épices (if used).

Pass the sauce through a fine-mesh sieve or chinois into a clean container, pressing on the solids with a ladle to extract all the liquid and flavor. Discard the strained solids.

Season the strained Espagnole sauce with salt and freshly ground black pepper to taste. If it's too thick, you can thin it with a little more warmed stock. If too thin, gently reduce it further over low heat until the desired consistency is achieved.