Mix graham cracker crumbs and melted butter together until it resembles wet sand. Press this firmly into a 9-inch springform pan, covering the bottom completely. I use the bottom of a measuring cup to pack it down evenly—makes a huge difference.
Whisk together sweetened condensed milk, vanilla extract, and the instant pudding mix in a large bowl. Stir until it thickens slightly, about 1-2 minutes. Don't overmix or you'll end up with pudding instead of the creamy custard layer you want.
In a separate bowl, whip heavy cream with powdered sugar until stiff peaks form. Gently fold the whipped cream into the pudding mixture—this is what makes your patriotic icebox cake family so light and airy instead of dense.
Spread half of this cream filling over your crust layer. Then drizzle the strawberry jam across the top and dollop half the blueberry compote over that. The berries sink in a little as it sets, which is exactly what you want.
Layer the remaining cream mixture on top, smoothing it out. Arrange fresh strawberries and blueberries on the surface in whatever pattern feels festive. I toss them with lemon juice first so they don't oxidize and turn brown.
Sprinkle chopped pistachios over the top for color and crunch. Cover loosely with plastic wrap and refrigerate for at least 4 hours, though overnight is better. The longer it sits, the more the flavors meld together—honestly, it's even better the next day.