Cut turkey, skinned side down, into 8 cutlets (see note). Cover with plastic wrap, and lightly pound cutlets with a meat mallet or bottom of a heavy skillet until inch thick. Season with salt and pepper.
In a large skillet, heat 1 tablespoon oil over high. Working in batches, cook cutlets until browned and opaque throughout, 2 to 3 minutes per side (add 1 tablespoon oil when needed). Transfer to a plate, and cover loosely with foil.
Add wine to skillet, and bring to a boil. Cook, scraping up browned bits with a wooden spoon, until reduced to 1/2 cup, 6 to 8 minutes. Whisk in Dijon; bring to a simmer. Remove from heat; stir in parsley, and season with salt and pepper. Top turkey with sauce.
To make slicing easier, freeze the meat for 20 minutes. Then, use a knife with a long, thin blade to slice the turkey breast on the diagonal into wide cutlets, and pound to desired thinness.