Bring a pot of well-salted water to a boil. Add the pasta and cook until al dente. Before draining, reserve around 1 cup of the pasta water.
While the pasta cooks, pat the prawns dry and season with salt and pepper. Place a large pan over high heat and add the olive oil and half the butter. Add the prawns in a single layer and cook for around 1 minute per side, until just pink and cooked through. Remove from the pan and set aside.
Add the remaining butter to the same pan. Add the garlic and chilli flakes and cook for 1 minute, until fragrant. Pour in the stock and scrape up the browned bits from the bottom of the pan. Simmer for 1 minute.
Add the cream and Parmigiano Reggiano. Mix well and simmer gently for 2–3 minutes, until glossy. Season to taste.
Add the drained pasta straight into the sauce with the prawns, any resting juices and ⅔ of the flat-leaf parsley (optional) and toss to coat. Add a splash of reserved pasta water as needed until the sauce is silky and clings to the pasta. Cook for 1 minute. If using, you can add some lemon zest here too.
Serve immediately with a squeeze of lemon juice, chopped parsley, extra chilli flakes, and Parmigiano Reggiano. Dig in.