Make a sachet by tying the parsley stems, thyme sprigs, bay leaf, and black peppercorns in a small piece of cheesecloth or wrapping tightly; set aside.
Melt the unsalted butter in a heavy 3β4 quart saucepan over medium heat. Sprinkle in the all-purpose flour and cook, stirring constantly, until the roux is a deep brown color that smells nutty, 6β8 minutes.
Add the finely chopped onion, carrot, and celery to the roux. Cook, stirring often, until the vegetables are well browned and lightly caramelized, 10β12 minutes.
Stir in the tomato paste and cook until it darkens slightly and smells sweet and roasted, 2β3 minutes.
Gradually whisk in the cold brown veal stock (unsalted), smoothing out any lumps. Bring to a gentle boil, then add the herb sachet.
Reduce to a bare simmer, uncovered, and cook 45β60 minutes, skimming foam and fat as needed, until reduced by about one-third and the sauce lightly coats the back of a spoon (nappe).
Remove and discard the sachet. Strain the sauce through a fine-mesh sieve, pressing lightly on the solids; discard solids. Degrease any surface fat.
Taste and season with kosher salt to taste. Use immediately, or cool rapidly and refrigerate up to 4 days or freeze for longer storage.