Bring a large pot of salted water to a rolling boil for the tagliatelle (salt it generously — it should taste like the sea). Salting the pasta water seasons the pasta internally as it cooks and ensures a balanced final dish. Use about 1 tsp kosher salt for 1.5–2 L water.

Prep the pork: pat the pork medallions dry with paper towel, then season both sides with 1/2 tsp kosher salt and 1/4 tsp freshly ground black pepper. Dry surfaces sear better and develop a golden crust; seasoning now begins flavoring the meat before cooking.

Bring the carrots to nearly tender: in a medium skillet over medium heat, add 1/2 tbsp olive oil and 1/2 tbsp butter. When the butter foams, add the halved baby carrots cut-side down. Sear undisturbed for 3–4 minutes until golden, then add 2–3 tbsp water, cover and steam 4–5 minutes until just tender. Finishing them this way gives a sweet, caramelized exterior while steaming ensures even doneness without burning.

Glaze the carrots: remove the lid, increase heat to medium-high, add a pinch of salt and the remaining 1/2 tbsp butter. Toss the carrots in the foaming butter 1–2 minutes to create a glossy glaze; spoon any buttery pan juices over them and set aside, keeping them warm. This concentrates their sweetness and gives a silky sheen for plating.

Cook the tagliatelle: add the dried tagliatelle to the boiling water and cook to 1 minute shy of package instructions (aim for al dente). Reserve 3/4 cup (180 ml) of the pasta cooking water before draining. Undercooking slightly ensures the pasta will finish perfectly in the sauce (carryover cooking) and the starchy water helps bind the cream sauce.

Sear the pork medallions: while the pasta cooks, heat a large heavy skillet (cast-iron or stainless steel) over medium-high heat with the remaining 1/2 tbsp olive oil. When the oil shimmers and just begins to smoke, add the pork medallions spaced apart. Sear undisturbed 1.5–2 minutes per side until a deep golden crust forms. Searing at high heat creates the Maillard reaction — those flavorful browned bits are essential for the sauce.

Finish the pork gently: after searing, lower heat to medium and add half the minced garlic (about 1 clove) to the pan, spooning the pan oil over the medallions for 30–45 seconds; this flavors the surface without burning the garlic. Transfer the medallions to a plate and loosely tent with foil to rest 5 minutes. Resting lets the juices redistribute so the pork stays tender and moist.

Make the lemon-garlic cream sauce: keep the skillet on medium heat, add the remaining 1 tbsp butter and the other minced garlic clove; cook 20–30 seconds until fragrant (blooming the garlic releases its aroma). Add the heavy cream and the juice and zest of 1/4 lemon, scraping any brown bits (fond) from the pan with a wooden spoon — those bits are concentrated flavor. Let the cream bubble gently for 1–2 minutes to thicken slightly.

Bring sauce to emulsion: add 2–3 tablespoons of the reserved pasta water and stir; then add the drained tagliatelle into the skillet and toss vigorously or use tongs to fold the pasta into the sauce for 1 minute. The starchy water helps emulsify the cream into a silky sauce that clings to the pasta. If the sauce seems too tight, add more pasta water, 1 tbsp at a time.

Finish and season: stir in chopped parsley, the remaining 1/4 tsp kosher salt (adjust to taste) and remaining 1/4 tsp black pepper to the pasta; toss again so the flavors marry. Taste and adjust lemon, salt, and pepper. A final splash of pasta water or a small pat of butter can round the sauce if needed.

Plate: divide the creamy lemon tagliatelle between two warmed plates. Arrange the rested pork medallions atop the pasta, spoon any resting juices from the pork over the medallions, and nestle the glazed baby carrots alongside. Finish with a light grate of lemon zest and a scatter of extra parsley for freshness and visual pop.

Serve immediately: serve hot. Encourage diners to cut the pork and twirl the pasta so every bite gets a little cream, lemon, and savory pork. Leftovers keep 1–2 days in the fridge; reheat gently with a splash of water or cream to restore the sauce.