Bring a large saucepan of salted water to the boil. Cook your pasta until al dente. Reserve 1/3 cup of the pasta cooking water, then drain the pasta and set aside.
Meanwhile, heat a large frying pan over medium heat. Add the broccoli florets and chicken stock and cook, stirring, for about 4–5 minutes (the stock will reduce quite a bit).
Add the cooked pasta and reserved pasta water to the frying pan and stir through. Then add the pesto and butter and stir until combined. Stir through the parmesan cheese, season well and serve.