Bring a large pot of salted water to a rolling boil (use about 1 L of water per 100 g pasta and 1 tsp salt). Salting pasta water seasons the pasta itself — if the water tastes like the sea, you’re at the right level. Keep the heat high so the pappardelle cooks evenly and doesn't stick.

While the water heats, season the chicken on both sides with 1/2 teaspoon salt and a few grinds of black pepper. Zest the lemon over the chicken, then squeeze the juice of half the lemon into a small bowl and stir with the minced garlic and half the chopped parsley. Brush or rub half of the olive oil (about 1/2 tbsp) and the lemon-garlic mixture over both sides of the chicken. This light marinade brightens the meat and the acid helps tenderize the thin cutlet.

Heat a heavy skillet or grill pan over medium-high heat until very hot — you want the pan hot enough to make a confident sizzle when the chicken hits it. Add a thin film of oil (you can use a quick spray or the remaining 1/2 tbsp olive oil) and swirl to coat. Sear the pounded chicken breast 3–4 minutes on the first side without moving it; this creates a golden-brown crust that adds flavor through the Maillard reaction. Flip and cook another 2–3 minutes until an instant-read thermometer reads 64–66°C (147–150°F). Because the breast is thin, it cooks quickly; remove it a few degrees before target as it will rise slightly while resting.

Transfer the chicken to a cutting board and tent loosely with foil to rest for 5 minutes. Resting lets the juices redistribute so the chicken stays moist when sliced.

Add the pappardelle to the boiling salted water and cook per package instructions (typically 7–9 minutes for dried pappardelle) until al dente — tender with a little bite. Reserve about 1/2 cup (120 ml) of the starchy pasta cooking water before draining; the starchy water will help marry the sauce and coat the pasta.

While the pasta cooks, return the same skillet to medium heat. Add the halved cherry tomatoes and cook, stirring occasionally, for 3–4 minutes until they begin to blister and soften — the blistering concentrates their sweetness and adds a touch of char flavor. Add the chopped kale and sauté for 1–2 minutes until it wilts but remains bright green; the quick cook keeps kale tender without losing structure. Stir in the minced garlic and cook 30 seconds just until fragrant (garlic burns quickly so brief cooking releases flavor without bitterness).

Pour the reserved pasta water into the skillet (start with 1/4 cup and add as needed) and bring to a gentle simmer — the water deglazes the pan and becomes the base of the light sauce. Add the drained pappardelle to the pan and toss to combine, adding the remaining lemon juice and lemon zest. Toss for 1–2 minutes over medium heat so the pasta absorbs some of the sauce; the starch in the water will make the sauce glossy and help it cling to the noodles.

Slice the rested chicken thinly on the bias (this increases tenderness and gives pretty presentation). Add the sliced chicken to the skillet or plate over the pasta. Stir in the grated Parmigiano-Reggiano and the remaining chopped parsley; the cheese melts into the warm pasta creating a silky coating and finishes the overall balance of acidity and fat. Taste and adjust salt and pepper.

Divide between two plates and finish with a light drizzle of extra-virgin olive oil if desired, a final grating of Parmigiano, and a few twists of black pepper. Serve immediately so the chicken remains warm and the pasta glossy.