Preheat oven to 350F. Line an 8x8 baking pan with parchment paper, criss-crossing two rectangular pieces so there is an overhang on either side for easy lifting. Set aside.
For the crust
In a medium sized bowl mix together the crumbs and butter with a spoon until moist. Press into the prepared pan and bake for about 10 minutes or until crust is set around the edges.
Meanwhile make the filling:
Beat together the white sugar, and cream cheese until smooth.
Add the egg, milk, lemon juice, and vanilla and beat until smooth and creamy. Spread filling mixture over baked crust.
For the Raspberry Purée:
In a food processor or blender, purée the raspberries until smooth. Press through a fine mesh sieve, getting as much liquid out as possible. Discard the solids. Stir in the sugar.
Dot the raspberry mixture over the filling and use a toothpick or skewer to swirl together.
Bake for 30 minutes or until set around the edges and slightly jiggly in the center. Cool completely on a wire rack and then chill until cold before serving.