Bring a large pot of salted water to a rolling boil for the pappardelle. Salting the water well (about 1–1.5% salinity) seasons the pasta from the inside as it cooks — you want the water to taste like the sea.

Pat the steak tips dry with paper towels and trim any large pieces of fat. Season generously on all sides with kosher salt and freshly ground black pepper. Dry meat sears better — moisture is the enemy of a good crust.

Heat a large heavy skillet (cast-iron or stainless steel) over medium-high heat until very hot. Add 2 tablespoons olive oil. When it shimmers, add half the steak tips in a single layer without crowding. Sear undisturbed for 1½–2 minutes per side until deeply browned. The Maillard reaction creates flavor compounds and color; quick, high-heat searing is essential.

Transfer the seared tips to a plate and repeat with the remaining 2 tablespoons oil and remaining steak tips. You want a brown crust but the interior will still be pink — this is fine because we'll quick-braise briefly.

Lower the heat to medium. Add the diced onion to the skillet (add a splash of oil if the pan looks dry). Sauté, stirring, until translucent and starting to color — about 3–4 minutes. Onions provide sweetness and a flavor base that balances the beef and wine.

Add the minced garlic and chopped mushrooms. Cook, stirring occasionally, until the mushrooms release their liquid and most of it evaporates and the edges start to brown, 5–6 minutes. Browning the mushrooms intensifies their earthiness and gives the sauce body.

Stir in the tomato paste and the chopped rosemary. Cook the paste for 1–2 minutes, stirring constantly, to 'toast' it — this removes the raw tinny flavor and deepens its sweetness and umami.

Deglaze the pan with the red wine (or beef stock if using). Pour it in and use a wooden spoon to scrape up the brown fond on the bottom of the pan — those browned bits are concentrated flavor. Increase heat to medium-high and reduce the liquid by about half (2–3 minutes) so the sauce becomes glossy and concentrated.

Return the seared steak tips and any accumulated juices to the skillet. Reduce heat to medium-low, cover partially, and simmer gently for 6–8 minutes, stirring once — this quick braise finishes the steaks and melts connective tissue just enough to tenderize without overcooking. The internal temperature should reach about 55–58°C (130–136°F) for medium-rare to medium when checked with an instant-read thermometer.

While the steaks braise, add the pappardelle to the boiling water and cook according to package directions until al dente (usually 7–9 minutes). Reserve 1 cup (240 ml) of the pasta cooking water before draining — starchy water helps marry the sauce to the pasta.

When the steak is done, remove the pan from heat. Stir in the tablespoon of butter (optional) to enrich and slightly thicken the sauce — emulsifying fat into the sauce makes it glossy and coats the pasta beautifully. Taste and adjust seasoning with salt and pepper.

Add the drained pappardelle directly to the skillet (or return both to the empty pasta pot). Toss with the sauce and steak tips, adding a splash or two of reserved pasta water as needed to loosen the sauce and help it cling to the noodles. The starch in the water binds the sauce to the pasta for a silky finish.

Serve immediately on warmed plates, finish with a grind of black pepper, a sprinkle of chopped fresh rosemary if desired and grated Parmesan or Pecorino at the table. Resting the dish briefly (1–2 minutes) lets flavors settle; cutting into the steak right away is fine because the pieces are bite-sized.