To make the filling, in a frying pan over medium heat, melt the butter. Add the onion and saute for 1 minute. Raise the heat to medium-high, add the garlic and spinach and saute until the spinach is wilted, 2—3 minutes. Stir in the sun-dried tomatoes. Transfer the spinach mixture to a colander and, using the back of a wooden spoon, press gently against the mixture to remove any excess moisture, then let cool. Wipe the frying pan clean and set aside.

Transfer the spinach mixture to a bowl. Stir in the Parmesan cheese and season to taste with salt and white pepper. Set aside. 

Place each chicken breast between 2 sheets of plastic wrap and, using a meat pounder, pound until ¼ inch thick. Place 1 cheese slice on top of each pounded breast. Spoon one-fourth of the spinach filling onto the bottom center of each cheese slice and shape the filling into a log, being careful that it does not protrude over the edges. Fold the sides in toward the center and then, beginning at the bottom end, roll up tightly. Secure with toothpicks. 

Preheat an oven to 425°F. In the frying pan over medium-high heat, warm the oil. While the oil is heating, spread the flour on a plate.

Roll the stuffed chicken breasts in the flour, coating lightly and evenly. Add the chicken to the pan and brown lightly on all sides, 5-7 minutes.

Using a slotted spatula, transfer the chicken to a baking dish. Place in the center of the oven and immediately reduce the heat to 375°F (190°C). Bake until cooked through, 10-12 minutes. Transfer to warmed individual plates and let stand for a few minutes. Remove the toothpicks. 11 While the chicken is baking, make the mushroom-wine sauce. In a small frying pan over medium heat, melt the butter. Add the onion and sauté until the edges begin to turn translucent, about 2 minutes. Add the mushrooms and saute until barely limp, about 2 minutes. Pour in the wine and deglaze the pan by stirring to dislodge any browned bits from the pan bottom. Cook over medium heat until the wine is reduced by half, about 2 minutes. Add the stock and simmer until reduced by half, 3—4 minutes. Pour in the cream and simmer until the sauce thickens slightly, 1—2 minutes. Season to taste with salt, white pepper and nutmeg.

Spoon the sauce over the chicken and serve immediately.