• Preheat oven to 300 degrees.
• Make foil sling for 13 by 9-inch baking pan by folding 2 long sheets of aluminum foil; first sheet should be 13 inches wide and second sheet should be 9 inches wide. Lay sheets of foil in pan perpendicular to each other, with extra foil hanging over edges of pan. Push foil into corners and up sides of pan, smoothing foil flush to pan. Spray with vegetable oil spray.

Base

• Process cracker pieces and sugar in food processor until finely ground, about 30 seconds. Add flour and salt and pulse to combine, about 2 pulses. Add melted butter and pulse until crumbs are evenly moistened, about 10 pulses.
• Using your hands, press crumb mixture evenly into bottom of prepared pan. Using bottom of dry measuring cup, firmly pack crust into pan.
• Bake until fragrant and beginning to brown around edges, about 20 minutes. Allow to cool completely.

Filling

• In clean, dry processor bowl, process cream cheese and sugar until smooth, about 3 minutes, scraping down sides of bowl as necessary.
• With processor running, add eggs, one at a time, until just incorporated, about 30 seconds total. Scrape down sides of bowl.
• Add vanilla and process to combine, about 10 seconds.
• Pour cream cheese mixture over cooled base.
• Bake until center is almost set but still jiggles slightly when pan is shaken, about 45 minutes.

Topping

• Meanwhile, in clean, dry processor bowl, process peaches and ¼ cup sugar until pureed, about 30 seconds.
• Stir puree and sour cream in bowl until blended.
• Remove cheesecake from oven. Pour peach mixture over cheesecake so it is completely covered.
• Return pan to oven and bake until topping is just set, about 15 minutes.
• Transfer pan to wire rack and allow cheesecake cool completely, about 2 hours.
• Refrigerate until cold and set, at least 4 hours or up to 24 hours.
• Using foil overhang, lift cheesecake out of pan and cut into 24 squares.