Bring a large pot of well-salted water to a boil for the pasta. Salting the water early seasons the pasta from the inside as it cooks and gives the final dish better flavor. Use about 1–1.5% salt by weight of the water (roughly 1 tablespoon per 4–5 liters).

Pat the thinly sliced flank steak dry with paper towels and season lightly with sea salt and a few grinds of black pepper. Drying the meat ensures it browns quickly; seasoning early helps the meat develop flavor during the quick braise.

Heat a large heavy skillet or sauté pan over medium-high heat and add 2 tablespoons of olive oil. When the oil shimmers (hot enough to sear but not smoking), add half the steak slices in a single layer—do not overcrowd the pan. Sear 45–60 seconds per side until just browned. Remove to a plate and repeat with the remaining steak. Searing creates Maillard flavors that deepen the final sauce; quick sears are enough because the steak will finish cooking in the jus.

Lower the heat to medium, add the remaining 2 tablespoons olive oil and the minced shallot (or red onion). Sauté 2–3 minutes until softened and translucent—this releases the aromatic base without browning too quickly. Add the minced garlic and cook 30 seconds more to bloom the garlic's aroma but avoid bitter burnt garlic.

Add the finely diced carrot and celery to the pan and sauté for 3–4 minutes until they begin to soften. Cooking the mirepoix briefly builds a gentle, sweet vegetable base that complements the beef without overpowering the pasta.

Pour in the red wine (or beef stock) and use a wooden spoon to scrape up any browned bits (fond) from the pan. Simmer briskly for 1–2 minutes to reduce the alcohol and concentrate flavor — this deglazing captures all the browned flavor into the sauce.

Stir in the halved cherry tomatoes and the balsamic vinegar. Bring to a simmer and let the mixture reduce lightly for 3–4 minutes until the tomatoes begin to break down and the sauce becomes glossy. The balsamic adds sweetness and acid to balance the beef, while the tomatoes add freshness and body.

Return the seared steak to the pan and fold into the sauce. Add a splash more water or stock if the sauce seems too thick; you want a silky jus that will cling to the pasta. Simmer gently for 2–3 minutes more — this quick braise finishes the steak and lets the flavors marry without overcooking the meat.

While the sauce simmers, cook the tagliatelle in the boiling salted water until al dente according to package instructions (usually 7–9 minutes for dry wide pasta; adjust if using fresh). Reserve 1 cup (240 ml) of pasta cooking water before draining. Starchy pasta water will help bind the sauce to the noodles and create a glossy finish.

Once the pasta is drained, return it to the pot off the heat and add the butter and 2–3 ladles of the reserved pasta water. Toss to melt the butter and loosen the noodles — this coating step helps the sauce cling to every strand.

Add the pasta to the skillet with the beef and vegetables and toss over low heat for 1–2 minutes, adding more reserved pasta water as needed to reach a silky, saucy consistency. Taste and adjust seasoning with sea salt, black pepper and an additional splash (½–1 tsp) of balsamic if you want brighter acidity. Tossing off-heat and finishing briefly on low ensures the beef stays tender and the pasta doesn't overcook.

Remove from heat, stir in the chopped basil and parsley (reserve a little for garnish), and finish with an extra drizzle of good olive oil and a grind of black pepper. Serve immediately, plating generous nests of tagliatelle topped with the balsamic-braised beef and a scattering of fresh herbs.