Heat the oil in a large skillet over medium-high heat.
Meanwhile, split the chicken breasts, butterflying them and cutting all the way through to make two thinner pieces.
Season the chicken with salt and pepper and brown, about 3 to 4 minutes per side, until golden.
Add the garlic and cook for 1 minute, until fragrant.
Add the cream, broth, parsley, salt, and pepper. Reduce the heat to medium and cook about 5 to 8 minutes, stirring often.
Cook until the sauce is thickened slightly, the chicken is cooked through and a meat thermometer inserted into the thickest part of the chicken reaches 165°F.
Taste and adjust seasonings as desired before serving.
