Pound the chicken until it is the same thickness all over and season with salt and pepper.
Heat a Dutch oven over medium-high heat with enough oil to coat the bottom.
Sear chicken in batches (2-3 minutes each side) until browned and mostly cooked through (it doesn’t have to be fully cooked), and set aside. Reduce heat to medium and melt butter.
Add the bell pepper and shallot, and sauté until mostly softened. If there is any fond on the bottom of the pan from searing the chicken, make sure to scrape that off the bottom as you go.
Add garlic and Cajun seasoning.
Cook for 30-60 seconds, until fragrant.
Add pasta and chicken stock.
Bring to a boil over medium-high heat, then reduce to medium. Cover and cook for 5 minutes.
Add heavy cream. Bring to a boil, then reduce to low and simmer for 5-8 minutes until pasta is al dente.
Dice chicken and add to the Dutch oven with lemon juice. Stir well.
Add salt and black pepper to taste.
Add Parmesan.
Stir until melted and sauce is creamy.
Serve hot, garnished with more Parmesan, parsley, and Cajun seasoning, if desired.