Combine ice cream, 3 tablespoons amaretto and 1 tablespoon brandy in large bowl. Stir to blend well. Cover and freeze until firm. (Can be prepared 2 days ahead. Keep ice cream mixture frozen.)
Combine peaches, sugar, remaining 2 tablespoons amaretto and remaining 1 tablespoon brandy in another large bowl. Toss to coat.
Let peach mixture stand until sugar dissolves, tossing occasionally, about 15 minutes.
Divide sliced peaches among 6 dessert bowls or wineglasses. Spoon vanilla ice cream mixture atop peaches.
