Season the chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken and cook for 6–7 minutes per side until golden and fully cooked. Remove and cover to keep warm.
In the same skillet, sauté the chopped onion for 3–4 minutes until soft.
Add garlic and cook for 1–2 minutes until fragrant.
Pour in the chicken broth, scraping up browned bits from the pan.
Let it simmer for 5 minutes to reduce slightly.
Add additional chicken broth and simmer again for 5 minutes.
Reduce heat to low and stir in the heavy cream slowly.
Add Dijon mustard and thyme, stirring until smooth.
Simmer for 3–4 minutes until the sauce thickens.
Adjust seasoning with salt and pepper.
Return the chicken to the skillet, spooning the sauce over it.
Simmer for 2–3 minutes to allow flavors to combine.
Stir in butter until melted.
Serve the Irish Chicken Cream Sauce Recipe topped with parsley.