Prepare the crust: In a large bowl, combine the crushed graham crackers or digestive biscuits, vanilla sugar, melted butter, and milk. Mix until the crumbs are evenly moistened.
Form the crust: Transfer the mixture to a 26 cm springform pan. Spread it evenly over the bottom and press firmly with your hand, spatula, or the bottom of a glass. Set aside.
Prepare the peaches: Wash, peel, and pit the peaches. Cut them into small pieces. Reserve 1 cup (150-170 g) of peaches for the topping.
Prepare the gelatin: Sprinkle the full packet of unflavored gelatin (about 6-8 g) over 50 ml cold water and let it bloom for a few minutes. Gently heat until completely dissolved, but do not boil. Divide the melted gelatin into two equal portions-one for the filling and one for the topping.
Whip the cream: In a large mixing bowl, whip the cold whipping cream until fluffy and firm
Make the peach yogurt filling: Add the peach yogurt, powdered sugar, vanilla sugar or vanilla extract, chopped peaches, and half of the prepared gelatin to the whipped cream. Gently fold until evenly combined.
Add the filling: Pour the peach yogurt mixture over the prepared crust and smooth the top with a spatula.
Chill briefly: Refrigerate the cake for about 20 minutes, or until the surface of the filling becomes slightly firm.
Make the peach topping: Place the reserved peaches and 200 ml water in a bowl or measuring cup. Blend with an immersion blender until smooth.
Finish the topping: Add the granulated sugar and the remaining half of the melted gelatin. Blend or stir until completely combined.
Add the topping: Slowly pour the peach mixture over the partially set yogurt layer, spreading it evenly over the top.
Chill: Return the cake to the refrigerator and chill for at least 4 hours, preferably overnight, until completely set.
Serve: Carefully remove the springform ring, slice the cake, and serve chilled.