In a bowl toss the peaches with 1/4 cup of the sugar and the lemon juice and let the mixture stand for 30 minutes. Drain the peaches and puree them in the food processor. In a heavy saucepan combine the remaining 3/4 cup sugar with 1/4 cup water, bring the mixture to a boil over moderate heat, washing down any sugar crystals clinging to the sides of the pan with the brush dipped in cold water, and simmer the syrup until it is pale golden caramel. Add the 1/2 cup boiling water carefully ( the mixture will bubble up) and simmer the syrup, stirring, until the caramel is dissolved.
In a small bowl sprinkle the cookies with the Amaretto and let stand for 5 minutes. In the large mixer bowl beat the egg yolks until they are thick and pale, add the syrup in a stream, beating, and beat the mixture until cool. Stir in the vanilla, peach puree, cookie mixture and cream. Freeze mixture in the ice cream freezer according to the manufacturer's instructions.
In a small heavy saucepan combine the cream and brown sugar, bring the mixture to a boil over moderately high heat, whisking occasionally, and whisk it until the brown sugar is dissolved. Remove the pan from the heat, add the bittersweet chocolate and the unsweetened chocolate, and whisk the mixture until the chocolate is melted. Whisk in the butter until the sauce is smooth and let the sauce cool slightly. The chocolate sauce may be make 1 week in advance and kept covered and chilled. Reheat the chocolate sauce over very low heat, stirring occasionally, until it is warm.
Yield: 3 cups