Preheat the oven to 350°F. While the oven heats up, process pretzels in a food processor or blender until they are very fine crumbs.
Combine crumbs with 4 tablespoons sugar and melted butter. Press into the bottom and up sides of a 9-inch pie plate. Bake for 15-20 minutes or until the edges are golden brown and the bottom is dry. Let cool to room temperature, about 30 minutes.
Purée peaches and 2 Tbsp. granulated sugar in a food processor until smooth. Strain the mixture through a fine mesh strainer, pressing on solids, to get ½ cup peach purée.
Sprinkle gelatin over ¼ cup cool water in a small microwave safe bowl; let stand for 5 minutes. Microwave for 10 seconds or just until melted, stirring as needed. Whisk into the peach purée.
Beat the egg whites, cream of tartar, and salt with an electric mixer at medium speed until foamy, about 2 minutes. Gradually beat in remaining 4 tablespoons sugar, 1 tablespoon at a time. Continue to beat until the egg whites reach medium peaks, about 2 minutes. Beat in vanilla.
Whisk about ¼ of the whipped egg whites into the peach mixture. Gently fold in the remaining egg whites.
Whisk jam briefly to loosen. Carefully spread jam on the bottom of the cooled crust in an even layer. Spoon chiffon filling on top of the jam, spreading evenly. Chill for 2 hours, or up to overnight. Serve with whipped cream and additional fresh peach slices, if desired.
