Preheat oven to 375ºF. In a medium sized bowl, mix together the peaches, sugar and amaretto. Macerate for 1/2 hour, stirring occasionally.
Slice each piece of brioche in half vertically, and lightly coat both sides of each piece with butter using a pastry brush. Place on a baking sheet and bake for 5-7 minutes. Turn slices over and bake for 5 minutes longer, or until brioche is toasted. Remove from oven and cool.
Drain liquid from peaches into a blender, reserving the peaches. Add 2 Tbsp. diced peaches to the blender and purée until smooth. Pour liquid back into bowl of peaches and mix together.
When ready to serve, slice the cheese into 24 thin slices. Top each brioche toast with a slice of the Le Brie de Chèvre and 1 tsp. of peach compote.