Cut the chicken breasts in half lengthwise and place in a bowl.
Add the flour, 1 teaspoon of salt, and pepper.
Mix the chicken until all sides are completely coated in the flour mixture. Set aside.
Heat 2 tablespoons of olive oil in a large skillet set over medium/high heat.
Add the chicken breasts and cook for 3-4 minutes on each side. Transfer the seared chicken to a clean plate and set aside.
Reduce the heat to medium and add the remaining tablespoon of olive oil to the skillet. Add the mushrooms, onions, and peppers and cook, stirring occasionally, until the onion is translucent and the veggies are softened, about 4-5 minutes.
Mix in the garlic, paprika, and thyme, and cook for an additional minute.
Add the wine to deglaze the pan and simmer for another minute.
Pour the broth into the skillet and add the cream cheese. Use a spoon or spatula to break the cream cheese apart so it begins to melt.
Transfer the chicken back into the pan and cook for another 4-5 minutes.
Serve with rice or pasta.