Melt the butter in a saucepan over medium heat, add the sliced peaches, brown sugar, and cinnamon, and cook for 5 to 7 minutes until the peaches soften and the juices turn glossy and syrupy.
Stir the lemon juice and salt into the peaches, then remove from heat and set aside, covered loosely, to stay warm.
Crack the eggs into a shallow baking dish, add the milk, sugar, vanilla, cinnamon, nutmeg, and salt, and whisk hard for 30 to 45 seconds until completely smooth.
Lay one slice of brioche in the custard for about 20 seconds per side, then lift and let the excess drip back into the dish.
Heat a skillet over medium heat with about 1/2 tablespoon of butter, then cook the soaked slices for 2 to 3 minutes per side until deep golden brown.
Wipe the pan and add fresh butter between batches, and move each finished slice to a wire rack rather than stacking them.
Arrange 2 slices on each plate, spoon the warm peach topping generously over the top, drizzle with maple syrup, and dust with powdered sugar if you like.