Divide the broccoli into small florets, peel the core and cut into thick slices. Finely chop the garlic.
Cook the pasta and broccoli together in a large pot: cook the pasta for 5 minutes, then add the broccoli and cook for a further 3 minutes (the total time of cooking spaghetti is 8 minutes). Drain pasta and broccoli, reserving 1/4 cup of pasta cooking water. Set aside.
Heat butter and olive oil in a large frying pan. When hot add garlic and red pepper flakes, cook, stirring for 30 seconds, until fragrant.
Whisk in pasta cooking water, lemon juice, lemon zest. Leave to cool for a minute then whisk in grated parmesan.
Add the broccoli and cooked pasta. Season with salt and pepper to taste. Toss until evenly coated. Add more lemon juice and red pepper flakes if necessary.
Enjoy!