Heat the butter and olive oil in a deep frying pan until they meld together.

Season each chicken breast with a pinch of salt and a dash of pepper.

Place the chicken breasts in the pan when the butter is melted and starts sizzling.

Cook them over high heat, allowing each side to brown for about 3-4 minutes until the chicken is beautifully browned

Remove it from the pan and set it aside.

Add the shallots into the same pan, and let them sizzle over high heat for a minute.

Add the garlic.

Cover the pan with a lid, reduce the heat, and let them gently cook for 5-10 minutes until the shallots turn soft and take on a delicate brown hue.

Pour in the wine, and let it come to a vigorous boil. Stir continuously for roughly 5 minutes until the liquid reduces by about two-thirds.

Time to add the mustard and cream to the mix. Stir well and let the flavors meld for 3-4 minutes until the sauce slightly thickens.

Season it with a bit of salt and a hint of pepper.

Bring the chicken breasts, along with any accumulated juices, back into the pan. Cover it again with the lid. Reduce the heat to a simmer and let everything simmer away for approximately 15 minutes. You'll know it's ready when the chicken becomes tender and fully cooked.

For serving, you can either plate each chicken breast as a whole or carve each chicken breast into three portions.

Spoon the dijon sauce over the chicken and garnish with a sprinkle of fresh chives.