Brown the Beef: Heat the olive oil in a large, heavy-bottomed saucepan or Dutch oven over a medium-high heat. Add the beef trimmings or mince. Cook for 8-10 minutes, breaking it up with a spoon, until the beef is deeply browned and crispy. Don't move it around too much at first; let it form a good crust.

Sauté the Aromatics: Add the chopped onion, carrot, and celery to the pan with the beef. Sauté for another 8-10 minutes, stirring occasionally, until the vegetables are soft and have started to caramelise and turn a rich brown colour. Add the minced garlic and cook for one minute more until fragrant.

Create the Roux (Optional): If you prefer a jus with a little more body, sprinkle the plain flour over the beef and vegetable mixture. Stir constantly and cook for 2 minutes. This cooks out the raw flour taste.

Deglaze the Pan: Pour the red wine into the pan. As it bubbles, use a wooden spoon to scrape all the browned bits from the bottom of the pan. This is where so much of the flavour lives! Let the wine reduce by about half, which should take 2-3 minutes.

Simmer the Jus: Pour in the beef stock and add the rosemary, thyme, bay leaf, and black peppercorns. Bring the mixture to a boil, then immediately reduce the heat to low.

Reduce and Infuse: Let the jus simmer gently, uncovered, for at least 30 minutes, or until it has reduced by about one-third and the flavour has concentrated. I find that a slow, gentle simmer is much better than a rolling boil for developing a clear, rich sauce.

Strain for a Smooth Finish: Carefully pour the jus through a fine-mesh sieve into a clean jug or saucepan, pressing down on the solids with the back of a spoon to extract every last bit of liquid. Discard the solids.

Season and Serve: Taste the finished beef jus and season with salt. Be careful, as it will have concentrated and may not need much. Reheat gently if necessary and serve hot as the ultimate French dip sauce or alongside a roast.