Start by heating your oven to 375°F so it's ready when you need it. Take each chicken breast and slice it horizontally, almost all the way through, so it opens up like a book. Gently pound it a little flatter with your palm or a mallet, then set the pieces aside on your cutting board while you make the filling.
Warm the olive oil in your skillet over medium-low heat, then toss in the garlic and onion. Cook them for a couple of minutes until they turn soft and fragrant. Stir in the chopped spinach, cranberries, thyme, salt, and pepper, and let everything cook down for about a minute until the spinach wilts. Pull the pan off the heat once it's ready.
Lay a slice of brie inside each opened chicken breast, then spoon a portion of the spinach and cranberry mixture right next to it. Fold the chicken back over the filling and wrap kitchen twine around it a few times to hold everything together. Repeat with the rest of the breasts, then sprinkle the outside of each one with a little extra salt and pepper.
Place your skillet back over medium-high heat with a touch more oil. Add the stuffed chicken breasts and sear them for about three minutes on each side. You're not trying to cook them through here, just building a golden crust that locks in flavor before they go into the oven.
Cover the skillet with foil or a lid and slide it into your preheated oven for about 25 minutes. Once the timer goes off, pull the chicken out and let it rest for five minutes before snipping away the twine. This little pause helps the juices settle back into the meat instead of spilling out the moment you cut it.