Clean mushrooms by wiping with a damp towel or brushing; trim stems and slice mushrooms into 1/4-inch slices so they cook evenly (about 4–5 cups sliced from 12 oz).

Crack peppercorns

Place peppercorns in a mortar and pestle or between two sheets of parchment and crush roughly so you have coarse fragments. Set aside.

Sear mushrooms

Heat a large skillet over medium-high heat. Add olive oil and 1 tbs butter. When butter is foaming and the pan is hot, add the sliced mushrooms in a single layer (work in two batches if necessary). Do not stir for 2–3 minutes so they brown, then stir or toss and continue cooking until golden-brown and any released liquid has mostly evaporated, about 6–8 minutes total per batch. Transfer browned mushrooms to a bowl and reserve.

Sweat aromatics

Reduce heat to medium. Add remaining 1 tbs butter to the same pan. Add minced shallot and cook until translucent, about 2 minutes. Add garlic and cracked peppercorns; cook, stirring, about 30 seconds until fragrant.

Deglaze

Add the dry red wine (1 tbs) to deglaze the pan, scraping up browned bits from the bottom with a wooden spoon. Let the wine reduce by half, about 1–2 minutes.

Build sauce

Return the mushrooms to the pan. Stir in tomato paste and cook for 1 minute to deepen flavor. Add beef stock (2 cups), thyme sprigs, soy sauce, and sugar (if using). Increase heat to bring to a gentle boil, then reduce to low and simmer uncovered until reduced by about one-third and slightly thickened, 12–18 minutes. Taste and adjust seasoning with salt as needed.

Finish and strain (optional)

For a smooth demi, remove thyme sprigs and strain the sauce through a fine-mesh sieve into a clean saucepan, pressing on solids to extract flavor. Return solids (optional) to use as garnish or discard. If you prefer a textured sauce, skip straining and continue with mushrooms in the sauce.

Enrich and adjust consistency

Over low heat stir in heavy cream (optional) for a silkier mouthfeel. If sauce needs more thickness, whisk in the prepared cornstarch slurry a little at a time while simmering until desired thickness is reached (about 1 tbs slurry will lightly thicken this volume). Re-warm gently but do not boil vigorously after adding cream.

Finish with butter (optional)

For a glossy finish, swirl in an extra 1 tbs of cold butter off the heat until melted.

Serve

Transfer mushroom pepper demi to a warm sauceboat or spoon over steaks, roasted meats, or mashed potatoes. Garnish with a few fresh thyme leaves and a sprinkle of cracked black pepper to taste.