Heat a small amount of the butter in a cast-iron skillet over medium-high heat.
Arrange the peach wedges in the hot skillet in a single layer. Sear for 2–3 minutes per side until lightly softened with golden, caramelized edges.
Transfer the peaches to a plate and reduce the skillet heat to medium-low.
Spread softened butter evenly over one side of each slice of sourdough, making sure to reach the edges for consistent browning.
Place one piece of bread in the skillet with the buttered side facing down.
Arrange half of the Brie over the bread. Layer the caramelized peach slices on top, followed by fresh thyme leaves, a small pinch of sea salt, and a light drizzle of honey.
Add the remaining Brie over the peaches. This helps hold the filling together as the cheese melts.
Place the second slice of sourdough on top with the buttered side facing upward.
Cook the Peach and Brie Grilled Cheese with Honey over medium-low heat for 3–5 minutes, until the bottom is deeply golden and crisp.
Carefully flip the sandwich with a wide spatula and cook for another 3–5 minutes. The bread should be evenly browned and the Brie soft and melted.
Remove the sandwich from the skillet and allow it to rest for 1 minute.
Slice diagonally and finish with additional fresh thyme and a small drizzle of honey before serving.