Beat eggs at medium speed of electric mixer until frothy. Gradually add 1 1/2 cups sugar, brown sugar, flour, and salt; beat well. Stir in milk and syrup. Cook over low heat until mixture begins to thicken, stirring constantly. Remove from heat. Chill thoroughly.
Combine peaches and 1/2 cup sugar; stir well. Stir peaches into custard. Add flavorings.
Beat evaporated milk until soft peaks form; fold into custard mixture.
Pour mixture into freezer can of a 1-gallon hand-turned or electric freezer. Freeze according to manufacturer's instructions. Let ripen at least 1 hour before serving.