Stir together flour and 1/4 teaspoon of the salt in a medium bowl. Add chicken cutlets, one at a time, and toss to coat evenly with flour. Shake off excess flour, and set aside on a plate.
Heat a large skillet over medium-high. Add butter and oil; cook, swirling occasionally, until butter is frothy, about 30 seconds. Add chicken in an even layer; cook, turning once halfway through, until browned and a thermometer inserted into thickest portion of breast registers 165°F, about 8 minutes. Transfer to a wire rack.
Add wine to skillet; cook over high, stirring occasionally and scraping bottom to release brown bits, until reduced by half, about 1 minute. Stir in stock, cream, black pepper, garlic, oregano, thyme, marjoram, and remaining 1/2 teaspoon salt. Bring to a simmer over medium-high; cook, stirring occasionally, until slightly thickened, about 4 minutes.
Stir in spinach; cook, stirring often, until spinach is wilted, about 1 minute.
Return chicken to skillet. Cook over medium-high, turning chicken once, until chicken is heated through, about 1 minute. Remove from heat; add basil and Parmesan, swirling to combine.
4 servings