Step 1: Prepare your peaches and raspberries. If using fresh peaches, peel, pit, and thinly slice them. If using canned, drain thoroughly and pat dry. Gently rinse fresh raspberries and pat dry. Set aside about half a cup of raspberries for garnish.
Step 2: In a large mixing bowl, combine the cold heavy cream, powdered sugar, and vanilla extract. Beat with an electric mixer on medium-high speed until stiff peaks form. Be careful not to overbeat.
Step 3: Line a 9x13 inch baking dish with parchment paper, leaving an overhang on the sides for easy removal, or simply grease the dish lightly.
Step 4: Arrange a single layer of vanilla wafers or graham crackers tightly at the bottom of the prepared dish, breaking some to fit as needed.
Step 5: Spread about one-third of the whipped cream evenly over the cracker layer.
Step 6: Place half of the sliced peaches evenly over the whipped cream, then scatter half of the remaining raspberries over the peaches.
Step 7: Create a second layer by placing more vanilla wafers/graham crackers over the fruit. Follow with another one-third of the whipped cream, then the remaining sliced peaches and raspberries.
Step 8: Top with a final layer of vanilla wafers/graham crackers. Spread the remaining whipped cream evenly over the top, smoothing it out.
Step 9: Cover the dish tightly with plastic wrap and refrigerate for at least 6-8 hours, or preferably overnight, to allow the wafers to soften and the flavors to meld.
Step 10: Before serving, remove the Peach Melba Icebox Cake from the refrigerator. Garnish with the reserved fresh raspberries and optionally a few extra peach slices or mint leaves. Slice and serve chilled.