Heat up your pan (or grill) to a medium-high heat.
Cut the loaf into 1-inch thick slices. Brush olive oil on both sides, and let it sear for 2-3 minutes on each side.
Cut the peaches in half and remove the pit. Lay the halves flat-side down and cut into 1/4” thick slices. Grill for 1 minute on each side.
Add balsamic vinegar in a saucepan over medium heat, stirring constantly. Bring to a boil, reduce heat to low, and simmer until glaze is reduced by half.
To assemble: top baguette slices with brie cheese. Add grilled peach and drizzle with balsamic vinegar. Garnish with arugula.