In a shallow, wide mouthed bowl, combine 2 tablespoons of parmesan and the flour. Pat the chicken dry with paper towels, and dip in the parmesan/flour on both sides until well coated. Shake off the excess, and place coated chicken on a plate.
In a large pan, melt 2 tablespoons of butter along with the vegetable oil over medium heat. Once shimmering, add the chicken and sear on each side until golden and the internal temp of your chicken reaches 165 F. Place cooked chicken aside on a plate and loosely tent with foil. {Psst--if your chicken is really thick, try placing a lid on top after you've seared each side, and reducing the heat of your pan to low to cook the chicken through.}
Add the remaining butter, once melted add the shallots and saute for 4 minutes, until they begin to soften. Add the garlic and saute until fragrant, about 1 minute.
Quickly add the chicken broth and bring to a simmer. Use the back of your spoon to scrap up any brown bits from the bottom of your pan, and allow the broth to reduce by half.
Add the heavy cream, remaining (1/4 cup) parmesan, Italian seasoning, salt, and pepper. Stir together and allow the cheese to melt into the sauce. Simmer until the sauce has slightly thickened, about 3 minutes.
Add the spinach, and cook until wilted.
Drizzle sauce over the cooked chicken breast, and enjoy!