Either pound chicken breasts with a meat mallet to 1/4" thickness, or carefully slice them in half, cross-wise so that you have 8 chicken breast halves.
Mix Panko and flour together in a shallow dish. Salt & pepper both sides of chicken and then press both sides into Panko mixture, to ensure it is well-coated.
Heat oil in a large skillet over medium-high heat, add chicken and cook 3-4 minutes on each side until browned, crisp, and cooked through (165 degrees F). Remove from skillet and keep warm.
Add wine to skillet and deglaze, scraping any browned bits. Add shallots and garlic and cook 30 seconds, then add cream and thyme and heat through. Add the chicken back to the pan to warm through with the sauce.
Serve the chicken with extra sauce.