Line an 9x9-inch baking pan with parchment paper, leaving few inches to overhang on all sides. Chill pan in the freezer until ready to use.
Make pistachio pudding. In a food processor, pulse pistachios until finely ground and nuts begin to turn into a paste, about 3 minutes. Add ¼ cup sugar (50 grams) and 2 tablespoons of milk. Continue to pulse until a thick paste forms.
Whisk together the pistachio paste and remaining 2 cups of milk until well combined. You can also blend the mixture together. Heat pistachio milk in a medium saucepot over medium-low heat until warm.
In a heat-safe bowl, whisk together egg, egg yolks, remaining ¼ cup (50 grams) sugar, and cornstarch. Slowly add pistachio milk, whisking constantly, until well combined. Pour mixture back into the pot and bring to a simmer over medium heat, stirring frequently. Continue to heat until pudding thickens, about 4-5 minutes. Remove from heat and add the butter, whisking until the butter melts and is fully incorporated. Transfer pudding to a bowl and cover with plastic wrap directly touching the surface to prevent a skin from forming. Let cool completely.
Whip 1 ½ cups of heavy cream with powdered sugar and vanilla in a large bowl until stiff peaks form. Add 1 cup to the pistachio pudding, folding in the cream until well combined. Set aside the remaining whipped cream.
Make raspberry cream. Whip 1 ½ cups heavy cream until stiff peaks form. Add ⅓ of the whipped cream to 1 cup of jam and whisk together until smooth. Fold in the remaining whipped cream, mixing until smooth.
Remove the prepared pan from the freezer. Line the bottom with graham crackers and spread half of the pistachio cream on top. Carefully spread ½ of the raspberry cream on top and lay another row of graham crackers. Repeat with the remaining pistachio cream and raspberry cream. Finish with the final layer of graham crackers.
Spread the reserved whipped cream on top of the crackers in an even layer. Add dollops of the remaining ¼ cup raspberry jam on top and swirl the jam into the whipped cream with a small spatula. Transfer the icebox cake to the freezer and let chill overnight or for at least 4 hours.
When ready to serve, garnish the pistachio and raspberry icebox cake with fresh raspberries and chopped pistachios. Slice and serve.