Slice each chicken breast lengthwise into two thinner pieces. Season both sides with salt, pepper, and garlic powder, then dredge in flour until evenly coated.
Heat the olive oil and 1 tablespoon of butter in a skillet over medium-high heat. Once the skillet is hot, place the chicken pieces in the pan and cook for 4–5 minutes on each side until golden brown. Remove the chicken and set aside; it does not need to be fully cooked at this stage.
Pour the white wine and chicken broth into the same skillet. Allow the mixture to bubble for about a minute, using a spoon to scrape up any browned bits stuck to the bottom of the pan.
Add the remaining butter along with the Herbs de Provence. Let the liquid simmer for an additional 2 minutes.
Pour in the cream and return the chicken to the skillet. Lower the heat to medium and cook for about 5 minutes, or until the chicken is fully cooked and the sauce has thickened slightly. Adjust seasoning with additional salt and pepper, if necessary. Garnish with fresh parsley before serving, if desired.