Start by laying your chicken breasts flat on a cutting board. Using a sharp knife, carefully slice a pocket into the thickest part of each breast, being careful not to cut all the way through to the other side. This creates a neat little space for our festive filling. Season the outside and the inside of the pockets with salt, black pepper, and smoked paprika for a hint of warmth.
Open each chicken pocket and place a generous spoonful of the spinach and cranberry mixture inside. Top the mixture with two or three slices of Brie cheese. To prevent the cheese from escaping during the cooking process, use two or three toothpicks to pin the edges of the chicken breast closed. Sprinkle the dried thyme over the tops of the prepared chicken.
Wipe out your skillet and add the remaining olive oil over medium high heat. Once the pan is hot, place the chicken breasts in and sear them for about 3 to 4 minutes per side until they are golden brown. This step locks in the juices and gives the chicken a beautiful color that looks great on the serving platter.
Transfer the skillet to a preheated oven at 375 degrees Fahrenheit. Bake for 12 to 15 minutes, or until the internal temperature of the chicken reaches 165 degrees Fahrenheit. Once done, let the chicken rest for five minutes before removing the toothpicks and serving. This resting period allows the cheese to set slightly so it does not all run out at once.