Slice the chicken breasts into two pieces, lengthways. Season with salt and black pepper.
Drizzle one tbsp of olive oil into the skillet and cook the chicken breast pieces for 5-6 minutes, each side, on a medium to high heat so you have browning (cook for longer if they are larger in size). Use tongs to remove from the skillet and set aside.
If the skillet seems dry, drizzle in a little more olive oil and take the heat down if needed. Saute the diced onion for 2-3 minutes, then add the garlic and cook for a further 2-3 minutes.
Pour in the chicken broth and sprinkle in the herbs de Provence. Stir well, then bring the heat of the skillet up a touch so it is lightly bubbling. Cook down the broth for 3-4 minutes. Use a wooden spoon to lift any brown bits from the pan.
Pour the heavy cream into the skillet, stir well, then place the chicken breasts back into the skillet. Cook for 4-5 minutes at a very light simmer (not a hard boil) to thicken the sauce, or until the chicken reads 165F at its deepest point using a meat thermometer. Season with salt and black pepper to taste, spoon onto your serving plate and sprinkle with fresh parsley.
