Horizontally slice both of the chicken breasts right through the centre to create 4 even-sized cutlets. In a zip-lock bag, whisk together the oil, lime juice and seasoning. Add the chicken and toss to combine, then lock the bag and leave to marinate in the fridge for as long as you have time for (up to overnight). If you're pushed for time, just rest at room temp as you prep the other ingredients. You can also do this in a bowl and cover with cling film.
Bring the chicken close to room temp if it was marinated in the fridge. Place a large deep pot or pan over medium-high heat. Once hot, add the cutlets and fry both sides for 3-4 minutes, or until lightly charred and piping hot/white right through the centre. Remove and place on a plate to one side. Slice into thin strips just before needed.
Add a drizzle more oil to the pan, then add the peppers and onion. Fry until soft and golden, then stir 1 tbsp fajita seasoning and fry for a minute longer. Stir in the tomato paste and fry for another minute or so, then pour in the stock, cream and pasta.
Give everything a good stir, then bring to a simmer, lower the heat and cook until the pasta is al dente. You'll want to stir fairly frequently to prevent sticking and try to keep the pasta submerged as best you can. If you run out of liquid before the pasta cooks, just add in a splash more stock or hot water to help cook it through. If you have any resting juices from the chicken, stir that in now for added flavour.
Turn the heat off and stir through the cheese until melted, then stir through the sliced chicken. Check for seasoning and adjust with salt, pepper and more fajita seasoning if needed (all brands will be different, so gradually work in the final 1/2 tbsp if you find it needs more).
Serve with a squeeze of lime juice and a sprinkle of coriander/cilantro or parsley, then tuck in and enjoy!