This recipe makes about 18 cookies.
To make Southern Peaches: Slice peaches, and put slices into a large mixing bowl. Sprinkle slices with sugar, salt and lemon juice. Set aside, covered, at room temperature.
Preheat oven to 350F. Lightly butter a large baking sheet, and set aside.
To make Pecan Shortbread: Cream butter, flour, sugar and salt in a large mixing bowl, using an electric beater, until dough is smooth and creamy. Add vanilla, and beat again. Stir in pecans. Pinch off a piece of dough, and roll into a 1-inch ball. Place on cookie sheet, and press flat with tines of a fork. Repeat with remaining dough.
Bake cookies until golden but not brown, for 12 to 15 minutes. Remove from oven, and, while still warm, sprinkle both sides with sugar. Set aside to cool.
To make Soft Whipped Cream: Put all ingredients into a chilled mixing bowl. Whip just until cream forms soft peaks, taking care not to overwhip. Keep refrigerated until ready to serve.
To serve, spoon portions of cut-up peaches on individual plates, place 2 cookies next to peaches and top with Soft Whipped Cream, if using.