Place chicken breasts between sheets of plastic wrap and pound with the flat side of a meat mallet until about 1/2-inch thick.
Heat a large skillet over medium-high heat and add the olive oil.
Season both sides of the chicken breasts with salt and freshly ground black pepper.
Place chicken in the hot skillet and cook undisturbed until golden brown on the bottom, about 6–7 minutes.
Flip the chicken and continue cooking until the internal temperature reaches 165°F (74°C), about 5–6 minutes more; remove chicken to a plate and tent with foil to keep warm.
Reduce heat to medium and melt the butter in the same skillet.
Add the minced garlic and sauté until just fragrant and lightly golden, about 20 seconds.
Sprinkle in the flour and cook, stirring constantly, until it is lightly golden, about 20 seconds.
While whisking, slowly pour in the milk, then add the diced cream cheese, minced thyme, and minced rosemary; season with a little salt and pepper to taste.
Keep whisking and cook the sauce until the cream cheese melts and the mixture comes to a gentle simmer and thickens slightly.
Return the chicken to the skillet and spoon the sauce over the pieces to coat and warm through.
Sprinkle with minced parsley if desired and serve immediately.