Pat your chicken breasts completely dry with paper towels, then season both sides generously with salt and pepper. Heat 1 tbsp olive oil in a large skillet over medium-high heat for about 2 minutes. You want it shimmering but not smoking. This is where the magic starts.
Place chicken breasts in the hot skillet and don't move them around—let them sear for 4-5 minutes until the bottom gets golden brown. Flip each piece carefully and sear the other side for another 4-5 minutes until both sides are golden. The inside doesn't need to be cooked through yet, just seared.
Remove the chicken to a clean plate and set it aside. You'll hear that satisfying sizzle when you add the butter to the pan next—that sound tells you the pan's at the perfect temperature. Add 2 tbsp butter and let it melt completely for about 30 seconds.
Add your Cajun seasoning, smoked paprika, garlic powder, onion powder, and cayenne pepper to the melted butter. Stir constantly for about 1-2 minutes to bloom those spices and wake up all those flavors. The spices should smell warm and toasty, not burnt. Keep the heat at medium so nothing burns.
Pour in 1/2 cup chicken broth and scrape the bottom of the pan with a wooden spoon to get all those brown bits. Those bits are pure flavor gold. Stir for about 1 minute, then add 1 cup heavy cream and whisk everything together until smooth. Don't rush this part.
Return the chicken breasts to the skillet and nestle them into the sauce. Add 1 cup frozen peas and carrots directly to the sauce around the chicken. Let everything simmer for 8-10 minutes until the chicken reaches 165°F internally (use a meat thermometer). When your kitchen smells like caramelized garlic and rich cream, you're almost done.
Remove from heat and stir in 1 cup shredded cheddar cheese until it melts completely into the sauce. Add 1 tbsp lemon juice and taste the sauce—adjust salt and pepper as needed. Finish with 1 tbsp fresh parsley scattered on top. I always taste and adjust as I go because that's how you nail the flavor.