Preheat oven to 350°F. Lightly spray an 8-inch springform pan with nonstick cooking spray.
Combine in a medium bowl graham cracker crumbs, butter, and sugar; stir to moisten crumbs. Press crust into bottom and slightly up sides of springform pan.
Bake in center of oven for 6 minutes or until crumbs just begin to brown. Remove from oven; cool. Leave oven on.
Purée peaches in mini food processor until smooth. Divide in half and set aside.
In mixer bowl, beat cream cheese on a medium speed; then, gradually add sugar and beat until smooth. Add eggs, one at a time; beat until light and whipped. Beat in vanilla, sour cream, and puréed peaches; then, stir in flour. Pour mixture into prepared crumb crust.
Wrap the bottom and sides of the springform pan in foil and set the pan on a baking sheet with sides. Set the baking sheet on the middle rack of oven, pour one half inch of hot water onto the baking sheet; then, carefully push the rack in and close oven door.
Bake for 10 minutes then reduce oven temperature to 325 F. Bake for one hour or until set. Cheesecake is done when a knife inserted in center comes out clean. The cake should still jiggle a bit when moved. Remove from oven and from the water bath and cool 45 minutes to one hour. Cover and chill until ready to serve.
Whisk sugar, cornstarch, and water together in a saucepot over medium heat and bring to a boil. Fold in reserved peach puree and peach slices, bring mixture back to a boil, stirring constantly; then, reduce heat and simmer 1 to 2 minutes or until sauce is thickened and translucent. Do not overcook the peaches. Stir in lemon juice, remove from heat, and cool. Chill until ready to serve.
To serve, arrange cooked peaches decoratively over top of cheesecake, allowing sauce to drip down the sides.
Fresh, frozen or even canned peaches, packed in juice or water, can be successfully used for this recipe.