Season chicken breasts all over with 1 teaspoon salt and ½ teaspoon pepper. Heat olive oil in a 12-inch heavy skillet over medium-high until shimmering. Add chicken and cook 4-5 minutes per side until golden brown and internal temperature reaches 160°F (carryover will take it to 165°F). Transfer to a plate; tent with foil.

Reduce heat to medium. Add butter to the skillet. Once melted, add onion and bell pepper. Cook 4 minutes, stirring occasionally, until softened and lightly browned.

Add garlic and cook 30 seconds until fragrant. Sprinkle Cajun seasoning over the vegetables and stir constantly for 45 seconds until the spices become fragrant and slightly darker – this is the bloom that deepens flavor and removes raw spice powder taste.

Pour in chicken broth. Scrape up any browned bits from the bottom of the pan. Bring to a simmer and let reduce by half, about 2 minutes.

Add heavy cream and remaining 1 teaspoon salt and ½ teaspoon pepper. Stir to combine. Bring to a gentle simmer, then add the dry pasta. Reduce heat to medium-low, cover, and cook 10-12 minutes, stirring twice, until pasta is al dente and sauce has thickened enough to coat the back of a spoon. If the sauce gets too thick before pasta is done, add a splash of warm water or broth.

While pasta cooks, slice the rested chicken into ½-inch strips.

Remove skillet from heat. Stir in Parmesan until melted. Add sliced chicken and any accumulated juices. Toss gently to combine. Let rest 2 minutes for sauce to settle.

Stir in parsley and lemon juice if using. Serve immediately.