Stir the graham cracker crumbs and melted butter together in a bowl until the crumbs are evenly moistened. Press the mixture firmly into the bottom of a 6-inch springform pan that fits inside your slow cooker.
Beat the cream cheese and sugar in a mixing bowl until smooth. Add the egg and vanilla extract, then mix until combined.
Pour in the melted white chocolate and beat again until the filling is creamy and uniform in color.
Gently fold the fresh raspberries into the filling, taking care not to crush them completely so you keep some whole pieces.
Spread the filling over the prepared crust and smooth the top. Cover the pan loosely with foil.
Set the pan inside the slow cooker and add enough water to reach about one inch up the sides of the pan. Cook on low until the center is just set.
Turn off the slow cooker, remove the pan, and let the cheesecake cool to room temperature before chilling it in the refrigerator.