Heat a small amount of the butter in a cast iron skillet over medium-high heat.
Arrange the peach wedges in a single layer. Sear for 2–3 minutes per side, or until the peaches develop caramelized golden edges and a light char. Transfer them to a plate.
Spread the remaining softened butter evenly over one side of each sourdough slice, taking the butter all the way to the edges.
Reduce the skillet heat to medium-low. Place one piece of sourdough in the skillet with the buttered side facing down.
Arrange half of the sliced Brie over the bread.
Add the caramelized peaches, fresh thyme, a small pinch of sea salt, and a drizzle of honey.
Arrange the remaining Brie over the peaches. Adding cheese on both sides helps hold the filling together as it melts.
Place the second slice of sourdough on top with its buttered side facing upward.
Cook the Peach and Brie Grilled Cheese with Honey for 3–5 minutes, or until the underside is crisp and deeply golden.
Carefully flip the sandwich and cook for another 3–5 minutes. Keep the heat medium-low so the bread browns gradually while the Brie has enough time to melt.
Remove the sandwich from the skillet and let it rest for about 1 minute.
Slice diagonally and finish with additional fresh thyme and a light drizzle of honey. Serve immediately.