Preheat the oven to 375°F. Dice the cream cheese into a few pieces and measure out the half-and-half. Let sit at room temperature while you start the recipe.

Place the flour in a shallow bowl (a pie plate works well). With tongs, lightly dredge each piece of chicken on both sides with flour, then transfer to a plate.

In a large, sturdy overproof skillet, heat 2 tablespoons oil over medium to medium-high heat. Add 2 tablespoons of the butter. Once the butter has melted, carefully lower 2 of the chicken breasts into the skillet (angle the chicken away from you to guard against spatters), ensuring they do not touch. Cook on both sides until golden brown, about 3 minutes per side. Transfer to a plate and cover to keep warm. The chicken will not be cooked through. Repeat with remaining chicken.

Reduce the pan heat to medium-low. Add the shallot to the now-empty pan. Cook, stirring occasionally, until the shallot is lightly caramelized, about 2 to 3 minutes.

Add the garlic and wine. Cook and simmer, scraping along the bottom of the pan, until the wine reduces by approximately half, about 1 minute.

Add the spinach by large handfuls, stirring so it wilts. Cook and stir until the spinach completely cooks down, about 4 to 5 minutes.

Turn off the heat. Add the diced cream cheese and half-and-half, stirring so that everything melts together smoothly. Stir in the Parmesan and sun-dried tomatoes. Stir in a pinch each of salt and black pepper, and the red pepper flakes (if using)

Return the chicken to the skillet, nestling it into the sauce. Transfer to the oven and bake until the chicken reaches 165°F on an instant read thermometer (I remove mine a few degrees early as the temperature will rise as it rests), about 10 to 15 minutes depending upon the size of your chicken breasts. If some finish earlier than others, transfer them to a plate and keep warm while you finish baking the rest. Serve the chicken hot with sauce spooned over the top.