Bring a large pot of water to a rolling boil and add 1 1/2 teaspoons kosher salt. Salted water seasons the pasta from the inside out; properly salted water should taste like the sea. Start the water first because it takes the longest to come to temperature.

While the water heats, butterfly each chicken breast (slice horizontally) so you have two thinner cutlets, or slice into 1/2-inch cutlets. Pat dry with paper towels and season both sides with 1 teaspoon kosher salt, a few grinds of black pepper, and 1/2 teaspoon dried oregano. Drying the chicken ensures a good sear; oregano adds a subtle savory note that complements garlic.

Heat a large skillet (preferably stainless steel or cast iron) over medium-high heat. Add 1 tablespoon olive oil and let it heat until shimmering but not smoking. Add the chicken; do not move it for 3–4 minutes. Searing on high heat develops a golden-brown crust and the Maillard flavor that makes the chicken deeply savory. If using thicker pieces, reduce heat slightly after browning to finish cooking through without burning.

Flip the chicken and add 1 tablespoon butter to the pan, tilting the pan and spooning the melted butter over the chicken for 1–2 minutes. This bastes the meat and adds richness. Cook until an instant-read thermometer inserted into the thickest part reads 160°F (70°C); carryover will bring it to 165°F. Transfer chicken to a cutting board and loosely tent with foil to rest for 5–7 minutes — resting allows juices to redistribute so the meat stays juicy when sliced.

When the water reaches a boil, add the pasta and cook 1–2 minutes less than package instructions for al dente (it will finish cooking in the sauce). Reserve 1 to 1 1/2 cups of the starchy pasta cooking water before draining. That starchy water is key: it emulsifies with butter and oil to create a silky sauce that clings to the pasta.

Reduce the skillet heat to medium. Add remaining 1 tablespoon olive oil and 2 tablespoons butter to the pan. Add the finely chopped onion and sauté 3–4 minutes until translucent; sweating the onion builds a sweet, savory base without browning. Add the minced garlic and 1/2 teaspoon red pepper flakes and cook 30–45 seconds until fragrant — garlic cooks quickly and will turn bitter if browned, so watch it closely.

Add about 3/4 cup reserved pasta water to the skillet and bring to a gentle simmer, scraping any browned bits from the pan (those bits are concentrated flavor). Simmer 1–2 minutes to slightly reduce. The water plus butter and oil will form an emulsion that becomes your sauce — it will thicken and coat the pasta.

Add the drained pasta directly into the skillet and toss vigorously with tongs for 1–2 minutes so the sauce clings to the strands. If the pasta looks dry, add more reserved pasta water a splash at a time until the sauce is glossy and coats the pasta. Emulsifying with hot starchy water is how classic restaurant kitchens get a silky finish without cream.

Slice the rested chicken thinly against the grain (this shortens fibers and yields tender bites). Add the chicken slices to the pasta and toss gently to combine and rewarm the chicken through for 30–60 seconds. Taste and adjust seasoning with salt and pepper if needed.

Divide onto warmed plates, garnish with chopped parsley if using, and serve immediately. Serving hot preserves the sauce’s emulsion and the chicken’s juiciness.