Season the chicken breasts on both sides with the salt and cracked pepper. The surface should look evenly coated so every bite gets flavor before it ever hits the skillet.

Set a large skillet over medium heat and melt 2 tablespoons of the butter. When the butter is fully melted and lightly foamy, the pan is ready for searing.

Lay the chicken in the skillet and cook for 4 to 5 minutes per side, then transfer it to a plate once cooked through. The chicken should look golden in spots and feel firm, and for best food safety it should reach 165 °F internally.

Add the remaining 1 tablespoon of butter to the same skillet, then stir in the garlic, fresh thyme leaves, and red pepper flakes for about 1 minute. You want a fragrant, buttery sizzle here, not dark garlic, which can turn the whole sauce bitter.

Pour in the heavy cream, sun-dried tomatoes, chicken broth, and Parmesan, then cook over medium heat while stirring often until the sauce thickens slightly; add salt to taste. The sauce is ready when the cheese has fully melted and the cream looks glossy, smooth, and lightly bubbling instead of oily or grainy.

Return the chicken to the skillet and spoon the sauce over the top. Let the chicken warm through in the sauce so the browned bits on the meat mingle with the cream.

Finish with fresh basil and serve with extra sauce over the chicken. The final skillet should smell garlicky and herby, with a soft red fleck from the tomatoes and peppers.