Sprinkle the chicken with salt and pepper. Dredge the chicken in the flour to coat lightly. Shake off any excess flour.
Melt 2 tablespoons of butter in a heavy large skillet over medium high heat. Add the chicken and cook until brown, about 5 minutes per side. You want the chicken to be just about cooked all the way through as it will continue cooking as it rests. Transfer the chicken to a plate and tent with foil to keep it warm.
Melt remaining 4 tablespoons of butter in the same skillet over medium heat. Add the mushrooms, shallots and garlic and saute until the shallots are translucent, stirring to scrape up any browned bits on the bottom of the skillet, about 1 minute.
Add the spinach, stir, and cook until wilted.
Add the wine. Increase the heat to medium-high and boil until the liquid is reduced by half, about 3 minutes.
Add the cream and simmer while the cream bubbles and reduces, stirring often, about 3 minutes.
Reduce heat to low and stir in the parmesan cheese, sun dried tomatoes and parsley. Season the sauce, to taste, with salt and pepper.
Add the chicken and any accumulated juices to the sauce, and turn the chicken to coat in the sauce.
Serve over pasta or mashed potatoes.