Bring a generous amount of water to boil and add a few fat pinches of salt
Pop in the spaghetti
Season the chicken pieces well with salt, pepper, and a tiny pinch of cayenne (red chilli powder)
Cook the chicken pieces in a hot skillet in the olive oil for about 2 minutes on each side on medium high heat - they should be golden brown and cooked through
Remove the chicken, turn down the temperature and then add the garlic and chilli flakes
Sprinkle on the flour and cook for a minute to take away the raw smell
Then whisk in the chicken stock, the lime zest, cream (start with ¼ cup) and some freshly ground pepper
Bring to a boil and simmer till it thickens a little
Add the chicken pieces and 2 tbsp lime juice to the sauce.
Drain the pasta when it's cooked through making sure to reserve a cup of pasta water
Add the sauce to the cooked spaghetti, stir to coat.
Now stir in the cheese, tossing the pasta frequently as you add it. It should melt into the pasta fairly quickly, add a splash of pasta water and additional cream to loosen the sauce if needed
Cook on medium heat stirring frequently until the sauce is a consistency you like. If it thickens too much then add more pasta water.
Add the cilantro, mix lightly and then taste the pasta - adjust seasoning with remaining lime juice, salt, pepper and chilli flakes