Butterfly the chicken breasts horizontally to make four even-sized pieces. In a ziplock bag or shallow dish, whisk together lime juice, oil, 1 tbsp Cajun seasoning, salt, and pepper. Add chicken, coat thoroughly, and marinate for at least 20 minutes (up to overnight).

Fry the chicken in a deep frying pan over medium-high heat for a few minutes on each side until lightly charred and cooked through. Remove from the pan and set aside to rest, then slice into thin strips.

In the same pan, fry the sliced mushrooms until they soften. Add the diced onion and peppers, frying until golden. Stir in the garlic for one minute, then add the remaining 1 tbsp Cajun seasoning and melt in the butter.

Pour in the chicken stock and heavy cream. Bring to a gentle simmer and allow to cook for about 10 minutes until the sauce begins to thicken.

While the sauce simmers, cook the penne in salted boiling water until al dente. Reserve one cup of starchy pasta water before draining.

Stir the Parmesan and parsley into the sauce, then season with salt and pepper to taste. Add the cooked pasta and sliced chicken (including any juices) to the pan. Toss until the sauce clings to the pasta, adding reserved pasta water if needed to thin the sauce.

Serve immediately with extra Parmesan, parsley, and an optional squeeze of lime juice.