Preheat your oven to 375°F (190°C) and make sure your ingredients are at room temperature for even cooking.
Prepare the chicken breasts by placing them on a cutting board and using a sharp knife to cut a horizontal pocket into the thickest part of each breast, being careful not to cut all the way through. Then gently pound the chicken with a meat mallet to even out the thickness.
Season inside each chicken pocket with salt, pepper, and a pinch of thyme leaves. This ensures the flavor permeates throughout the chicken, not just on the outside.
Stuff each chicken breast with a portion of brie and about 2 tablespoons of chopped cranberries. Gently press the openings closed and secure with toothpicks if needed.
Season the outside of the chicken breasts generously with salt and pepper on both sides. This creates a flavorful crust when searing.
Heat olive oil and butter in an oven-safe skillet over medium-high heat until the butter is melted and slightly bubbling.
Carefully place the stuffed chicken breasts in the hot skillet and sear for 3-4 minutes per side until golden brown. Work in batches if needed to avoid overcrowding the pan.
Add minced garlic around the chicken and cook for 30 seconds until fragrant, being careful not to burn it.
Pour in the white wine (or broth) and add the Dijon mustard, stirring to combine with the pan juices. Sprinkle the remaining thyme over the chicken.
Transfer the entire skillet to the preheated oven and bake for 15-18 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) when tested with a meat thermometer.
Remove from the oven and let rest for 5 minutes before serving to allow the juices to redistribute throughout the meat.
Garnish with fresh parsley and spoon the pan sauce over each chicken breast before serving.