Preheat your oven to 400°F (200°C).

Place each chicken breast on a cutting board. Using a sharp knife, carefully butterfly each breast by slicing horizontally through the thickest part, being careful not to cut all the way through, so it opens like a book. Cover with plastic wrap and pound evenly to about 1/2-inch thickness using a meat mallet or the bottom of a heavy pan. This ensures even cooking and easier rolling.

Season both sides of the pounded chicken breasts with 1/2 tsp salt, 1/4 tsp black pepper, and 1/2 tsp paprika.

In a large oven-safe skillet (or a separate pan if your skillet isn't oven-safe), heat 1 tbsp olive oil and 1 tbsp butter over medium heat. Add the finely chopped mushrooms and cook for 5-7 minutes until they release their moisture and start to brown. This is key for flavor.

Add the minced shallot and garlic to the skillet, cooking for another 2-3 minutes until fragrant and softened.

Stir in the chopped fresh spinach. Cook until the spinach wilts down, about 1-2 minutes. Remove the skillet from the heat.

Transfer the mushroom mixture to a medium mixing bowl. Add the softened cream cheese, grated Parmesan cheese, chopped fresh parsley, and chopped fresh thyme. Mix well to combine. Season with salt and black pepper to taste.

Lay each pounded chicken breast flat. Spoon about 1/4 of the mushroom stuffing onto one side of each breast, leaving a small border. Carefully roll or fold the chicken breast over the stuffing to enclose it. Secure the seam and sides with 2-3 toothpicks per breast to prevent the stuffing from leaking out.

Heat 1 tbsp olive oil in the same oven-safe skillet (or a clean one) over medium-high heat. Once hot, carefully place the stuffed chicken breasts, seam-side down, into the skillet. Sear for 3-4 minutes per side until golden brown and a crust forms.

Transfer the skillet with the seared chicken breasts to the preheated oven. Bake for 15-20 minutes, or until the internal temperature of the chicken reaches 165°F (74°C).

Carefully remove the chicken from the oven and transfer to a clean cutting board. Tent loosely with foil and let rest for 5-10 minutes. This allows the juices to redistribute, keeping the chicken moist. Remove toothpicks before serving.

While the chicken rests, place the same skillet back on the stovetop over medium heat (if there are excess chicken bits, you can drain some fat, but keep the browned bits for flavor). Add 1 tbsp unsalted butter and melt.

Whisk in 1 tbsp all-purpose flour and cook for 1 minute, stirring constantly, to create a roux.

Gradually whisk in the chicken broth, scraping up any browned bits from the bottom of the pan. Bring to a simmer, then whisk in the heavy cream and Dijon mustard. Cook, stirring occasionally, until the sauce thickens slightly, about 3-5 minutes.

Season the sauce with salt and black pepper to taste. If too thick, add a splash more broth; if too thin, simmer a bit longer.

Slice each stuffed chicken breast into thick medallions or serve whole. Spoon the warm creamy pan sauce generously over the chicken. Garnish with fresh chopped parsley, if desired. Serve immediately with your favorite side dishes like roasted vegetables, mashed potatoes, or rice.