Heat the olive oil in a large pan over medium heat. Add the chicken and sear for 3-4 minutes per side, or until golden brown and cooked through to an internal temperature of 165°F. Reduce the heat to low if it looks like the chicken is browning too quickly so that the pepper doesn’t burn. Transfer to a cutting board and let rest, slicing just before serving.

Meanwhile, bring a large pot of heavily salted water to a boil. Add the pasta and cook until just shy of al dente. Before draining, reserve 1 cup of the starchy pasta water.

Pour the reserved pasta water directly into the pan used to cook the chicken, scraping up any browned bits from the bottom. Bring to a gentle simmer.

Reduce the heat to low. Add the cold butter a few cubes at a time, stirring continuously and allowing each addition to emulsify into the pasta water before adding more. At this point, the sauce will still be fairly thin but will continue to thicken as the pasta finishes cooking.

Add the pasta directly to the pan. Toss continuously for 1-2 minutes, allowing the pasta to finish cooking and the sauce to thicken slightly.

Remove the pan from the heat. Add the lemon zest and Parmesan, then toss quickly until the cheese melts and the sauce is smooth and glossy.

Serve the pasta into bowls with the sliced chicken on top. Finish with some Parmesan, freshly cracked black pepper, and more lemon zest, if you’d like.