Boil a pot of heavily salted water and cook the rigatoni to package instructions. Add the broccoli to the same pot at the start and cook for a couple of minutes - remove with a slotted spoon and chop into small pieces. Set aside.
While the pasta cooks, melt the butter in another pot on medium heat. Once melted add the flour and, stirring constantly, cook for a few minutes until the raw flour smell is gone and replaced with a more nutty one.
Turn the heat down and start adding in the milk, a few splashes at a time. You want to very gradually add the milk to avoid lumps, so just add a little at a time and whisk to combine. I just use milk straight from the fridge - no need to pre-heat! The key to lump-free béchamel is adding the milk in little by little.
Add the gochujang and a pinch of salt and pepper .f you're worried about spice add a tablespoon and a half of gochujang to begin with. Keep mixing until combined.
One handful at a time, add in the grated cheddar. Stir to combine and once completely melted add in the next handful and repeat until all of the cheese is added.
At this point you want to taste the sauce for seasoning and add more gochujang and/or cheese to taste.
Once tasting perfect, add the chopped broccoli and drained rigatoni. Stir to combine until the pasta is completely coated in the glossy sauce.
To serve, top with chopped spring onion (don't skip this!) and sesame seeds.