Put oven rack in middle position and preheat oven to 350 degrees. Melt 2 Tbsp. butter and pour into a 13 x 19 inch glass or ceramic baking dish. Pulse 3/4 cup crumbled amoretti in a food processor until finely chopped, then add flour, sugar, salt, and remaining 2 Tbsp. butter. Blend until butter is incorporated, then add egg and blend until smooth.
Scoop out just enough peach pulp from center of each peach half with a melon ball cutter or small spoon to create a 1" deep cavity. Arrange peaches, cut sides up, in baking dish, then brush skins with melted butter from dish. Divide amaretti mixture among cavities, then sprinkle remaining 1/4 cup crumbled amoretti over filling. Bake until filling is puffed and crisp, 40 to 50 minutes. Serve warm or at room temp.
Wisk mascarpone with a few tablespoons of milk until it reaches a consistency suitable to dollop on peaches. Spoon on 1 Tbsp. per peach.