Preheat the oven to 375°F (190°C). Cut the chicken breasts lengthwise into 6 smaller pieces suitable for butterflying. Slice each piece lengthwise through the middle without cutting all the way through, then open it flat and gently tenderize it.
Heat a large oven-safe skillet over low-medium heat and add half of the oil.
Add the minced onion and garlic. Sauté until the onion becomes translucent, stirring occasionally.
Add the chopped spinach, dried cranberries, thyme, salt, and black pepper. Cook for about 1 minute, then remove the skillet from the heat.
Divide the spinach mixture into 6 equal portions.
Place a slice of Brie and one portion of the filling in the center of each opened chicken piece. Fold the chicken over the filling, tucking in the ends when possible.
Secure each piece tightly with kitchen twine. Season the outside with a little additional salt and pepper.
Return the skillet to medium heat and add the remaining oil. Sear the stuffed chicken for approximately 3 minutes per side until lightly golden.
Cover the oven-safe skillet, or transfer the chicken to a covered baking dish. Bake for about 25 minutes, or until the chicken reaches a safe internal temperature of 165°F (74°C) at the thickest part.
Remove the chicken from the oven and let it rest for 5 minutes. Carefully remove the kitchen twine before serving.
Serve hot with your favorite side, spooning some of the pan juices over the chicken.