Bring a large pot of salted water to a vigorous boil (use about 1 tbsp salt per 4–5 liters). Salted water seasons the pasta from the inside and gives the sauce a better final balance.

While the water heats, heat a wide sauté pan or shallow saucepan over medium-high heat and add 1 tbsp extra-virgin olive oil. When the oil shimmers, add the finely diced carrot and chopped onion. Turn the heat to medium and sweat them gently for 5–6 minutes until they soften and begin to color slightly. Sweating (rather than blasting with high heat) draws out sweetness from the vegetables and builds the flavor base — this is your quick soffritto.

Add the minced garlic and cook for 30–45 seconds until fragrant. Garlic burns quickly; adding it after the vegetables prevents bitterness and lets it perfume the oil.

Increase the heat to medium-high and add the lean ground beef, breaking it into bite-sized pieces with a wooden spoon. Spread it into an even layer and let it sear, undisturbed, for 2–3 minutes to develop Maillard browning. Then stir and continue to brown until no pink remains (another 2–3 minutes). Browning the meat creates deep, savory flavors — don't rush this step.

Season the meat lightly with salt and a few grinds of black pepper. If using red wine, pour in 1/4 cup (60 ml) to deglaze the pan, scraping up any browned bits (fond) from the bottom — those bits add concentrated flavor. Allow the wine to reduce by half (~2 minutes). If you prefer not to use wine, add 1/4 cup vegetable stock instead and let it reduce slightly.

Add the canned cherry or crushed tomatoes (120 g). Break any whole cherry tomatoes with your spoon so they integrate evenly. Lower the heat to medium-low and simmer, uncovered, stirring occasionally, for 10–12 minutes until the sauce thickens slightly and the flavors concentrate. This shorter simmer (compared to a long ragù) still allows the tomatoes to cook down and meld with the beef.

Stir in the sliced olives and chopped rosemary in the last 2 minutes of cooking so their brightness and texture remain lively. Taste and adjust seasoning with salt and pepper — olives are salty, so check before adding more salt.

When the water reaches a rolling boil, add the pappardelle and cook according to package directions minus 1 minute (usually 6–8 minutes for fresh/dried pappardelle; adjust to package). Reserve 1 cup (240 ml) of the starchy pasta cooking water before draining. Reserving water is essential: the starch helps emulsify and thicken the sauce so it clings to the pasta.

Drain the pasta and add it directly to the pan with the ragù over low heat. Add 2–4 tbsp of the reserved pasta water and toss vigorously with tongs or two forks for 1–2 minutes until the sauce emulsifies and becomes glossy, coating each ribbon. If the sauce seems dry, add more pasta water a tablespoon at a time. Finishing pasta in the pan lets the sauce penetrate the noodles and creates a cohesive dish.

Remove from heat, stir in the chopped parsley, taste for final seasoning, and plate immediately. Finish with a drizzle of good extra-virgin olive oil and an extra grind of black pepper if desired.