Stack cutlets in a double layer in a 1-gallon freezer bag. In a small bowl, combine 2 tablespoons butter, wine, garlic, and thyme and whisk to combine. Season with pepper. Pour marinade into bag with cutlets and freeze (see below).
To serve, thaw chicken in refrigerator overnight. Remove cutlets from bag and discard marinade. Gently shake chicken to remove liquid and season with salt. In 2 batches, heat 1 1/2 teaspoons butter and 1 1/2 teaspoons oil in a large skillet over medium-high; add half the cutlets to pan and cook until browned and cooked through, 4 minutes total, flipping halfway through and adjusting heat as necessary to prevent pan from overbrowning. Serve chicken sprinkled with parsley, if desired.
To freeze, press air out of freezer bag, seal, and freeze flat. Store in the freezer, up to 2 months.