Mix the flour, Parmesan, and salt and pepper on a plate and dredge the chicken breasts to coat.
Heat a large pan over medium with olive oil and 2 tablespoons butter, cook the chicken until golden but not cooked through, then remove and set aside.
Melt the remaining butter in the pan, add the shallot, garlic, and a pinch of salt, and cook until softened.
Deglaze with wine and broth, scraping up the browned bits, and let reduce by half with the basil and oregano.
Stir in the cream and cream cheese until thickened, fold in the spinach until just wilted.
Return the chicken to the pan and simmer until cooked through before serving with freshly grated Parmesan.
