Season the chicken breasts generously with salt and black pepper on both sides to enhance their natural flavors.
Heat olive oil in a large skillet over medium-high heat and add the seasoned chicken breasts. Cook for about 6-7 minutes on each side until they are golden brown and cooked through, then remove them from the skillet and set aside.
In the same skillet, add butter until melted, then toss in finely chopped onions and minced garlic. Sauté for about 3-4 minutes until onions become translucent and fragrant.
Pour in the Irish barley tea, carefully igniting it with a long match or lighter if desired, allowing any residual alcohol to cook off.
Once reduced slightly, stir in heavy cream along with Dijon mustard, Worcestershire sauce, and chicken broth. Bring this mixture to a simmer while stirring continuously until it thickens beautifully.
Return the seared chicken breasts back into the skillet, spooning sauce over them before letting them simmer together for another 5 minutes so they can absorb all those luscious flavors.