Season both sides of each piece of chicken with salt and pepper.
Place the flour in a shallow bowl and coat both sides of each piece of chicken. Set aside.
Melt the butter and oil in a skillet set over medium-high heat. Add the chicken and cook until both sides are golden brown, about 3-5 minutes per side. Remove the chicken from the pan and set aside.
Add the onion and cook until translucent, about 5 minutes. Add the garlic and cook until fragrant.
Pour in the white wine to deglaze the pan, scraping up any brown bits from the bottom of the pan. Simmer to reduce for 1-2 minutes.
Stir in the chicken broth, heavy cream, Parmesan, lemon juice, salt, and pepper. Return the chicken to the pan and simmer in the sauce until cooked through, about 5 minutes. Serve with lemon wedges and parsley.
