In a mortar and pestle or a Ziplock bag crush the herbs de Provence herb mixture until fragrant. Mix together in a small bowl with the heavy cream, chicken stock, lemon zest (not juice), and dijon mustard. Set aside
In a pan over medium low heat, melt the butter. Place the chicken breasts skin side down into the pan and cook for 7-10 minutes, or until the skin is a deep golden brown. Flip and pour the sauce and lemon juice into the pan.
Transfer the pan into the oven and bake for 20-30 minutes or until the thickest part of the chicken breast is 160°F.
Remove the chicken from the oven and transfer the chicken to a plate. Put the pan over medium heat and reduce the sauce by half. Remove it from the heat and swirl in the butter to emulsify the sauce. Return the chicken to the sauce, simmer for another minute then serve.
Notes
Make sure you have an oven-safe pan that goes from the cooktop into the oven. This helps preserve all the good flavors in the sauce.
To get crispy skin on the chicken breasts, take your time and cook at a lower temperature. If you prioritize cooking quickly, the skin will burn in parts while others are still sticking to the pan because they aren't finished.
Keep in mind that the butter will only bind the sauce for the original cooking. If you refrigerate and reheat leftovers, the sauce needs this process to be done again to re-emulsify it.
Make sure the butter for the lemon cream sauce is COLD. If it is room temperature it will melt too quickly and not emulsify.
If you have a probe thermometer that is oven safe, you'll have the best control over keeping the chicken breasts moist.