For Crust: Preheat oven to 350 degrees F. Add butter to graham cracker crumbs and stir until evenly moistened. Press crumbs over bottom and 1 inch up sides of a 9-inch-diameter springform pan with 2 3/4-inch-high sides. Bake crust until beginning to brown, about 8 minutes. Cool on rack. Reduce oven temperature to 325 degrees F.
For Filling: Combine peaches, 2 tablespoons sugar, and lemon juice in heavy large saucepan. Cover and cook over medium-high heat until sugar dissolves and peaches are juicy, stirring occasionally, about 5 minutes. Uncover and cook until peaches are tender and juices thicken, about 5 minutes. Cool compote.
Using electric mixer, beat cream cheese in large bowl until fluffy. Gradually add 1 1/4 cups sugar and beat until smooth. Beat in eggs 1 at a time. Mix in sour cream and vanilla. Spoon half of cheese mixture (about 3 cups) into crust. Spoon peach compote over by tablespoonfuls, spacing apart. Top with remaining cheese mixture.
Place large piece of foil on oven rack. Place pan with cheesecake on foil. Bake until puffed, set in center, and beginning to brown, 60 to 75 minutes, until brown on top and center is set. Place hot cheesecake on rack; cool 5 minutes. run small sharp knife around pan sides to loosen. Place cheesecake, uncovered, on rack in refrigerator and chill overnight. (Can make up to 2 days ahead. Cover and keep chilled.)
For Glaze: combine preserves and lemon juice in heavy small saucepan. Stir over medium heat until glaze comes to simmer. Strain into small bowl. Release pan sides; place cheesecake on platter. Spread glaze over top of cheesecake to within 1/4 inch of edge. Chill cheesecake until glaze sets, at least 30 minutes and up to 8 hours. Arrange peach slices in center of cake and serve.
Note: This recipe has been updated since original posting to add an optional 15 minutes of baking time. I realized my oven temp was off at the time of original posting. Please bake until beginning to brown on top and center is set.
To prevent cheesecake from splitting on top, place a shallow pan of water into the oven while cheesecake is baking.