Prep the chicken: Pat the chicken dry. Using a sharp knife, slice a pocket horizontally into the thickest side of each breast, stopping about 1/2 inch from the other side. Don’t cut through.
Season the outside with salt, pepper, and smoked paprika.
Cook the mushroom filling: Heat 1 tablespoon olive oil and the butter in a skillet over medium-high heat. Add mushrooms and cook, stirring occasionally, until they release liquid and start to brown, 6–8 minutes.
Add aromatics: Stir in shallot, garlic, thyme, and oregano. Cook 1–2 minutes until fragrant.
Season with a pinch of salt and pepper. Remove from heat and let cool 2–3 minutes.
Make it creamy: In a bowl, combine the warm mushroom mixture with cream cheese, Parmesan, and parsley. Mix until smooth and spreadable.
Taste and adjust salt if needed.
Stuff the chicken: Spoon the filling into each pocket, dividing evenly. Don’t overfill. Secure the opening with toothpicks to keep the filling inside.
Sear for color: Wipe out the skillet if needed.
Add the remaining 1 tablespoon olive oil and heat over medium-high. Sear chicken 2–3 minutes per side until golden.
Finish in the oven: Transfer the skillet to a preheated 375°F (190°C) oven, or move the chicken to a baking dish. Bake 12–18 minutes, depending on thickness, until the internal temperature hits 165°F (74°C).
Rest and serve: Let the chicken rest 5 minutes.
Remove toothpicks, garnish with parsley, and add a light squeeze of lemon if you like.