Slice the chicken breasts horizontally to create four thinner cutlets. In a shallow dish, combine the flour, garlic powder, salt, and pepper. Lightly dredge each chicken cutlet in the flour mixture, ensuring it's evenly coated but shaking off any excess.

In a large skillet over medium-high heat, melt the butter with the olive oil. Once hot, carefully place the chicken in the skillet. Cook for 4-5 minutes per side, or until golden brown and cooked through (internal temperature reaches 165°F / 74°C). Remove the chicken from the skillet and set aside on a plate.

Reduce the heat to medium. Add the minced garlic to the same skillet and cook for about 30-60 seconds until fragrant, being careful not to burn it. Pour in the chicken broth to deglaze the pan, using a wooden spoon to scrape up any flavorful browned bits from the bottom.

Stir in the heavy cream and bring the mixture to a gentle simmer. Let it cook for 2-3 minutes, stirring occasionally, until the sauce begins to thicken.

Reduce the heat to low. Stir in the freshly grated Parmesan cheese and the chopped fresh herbs (parsley, thyme, rosemary). Continue stirring until the cheese has melted completely and the sauce is smooth. Return the cooked chicken to the skillet, spooning the sauce over it. Let it simmer gently for another minute for the flavors to meld. Serve immediately.