Prepare the Cake:
Preheat the oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
In a bowl, whisk together flour, baking powder, and salt.
In a separate large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Gradually add the flour mixture alternately with milk, starting and ending with flour.
Divide the batter evenly between the prepared pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Cool in the pans for 10 minutes, then turn out onto wire racks to cool completely.
Make the Raspberry Filling:
Combine the raspberries, sugar, cornstarch, and water in a saucepan over medium heat. Cook, stirring constantly until the mixture thickens and comes to a boil. Allow to boil for 1 minute, then remove from heat and cool completely.
Prepare the Cream Cheese Frosting:
Beat the cream cheese and butter together until smooth. Gradually add powdered sugar and vanilla, beating until the frosting is smooth and spreadable.
Assemble the Cake:
Place one cake layer on a serving plate. Spread a layer of cream cheese, followed by half of the cooled raspberry filling.
Top with the second cake layer, and repeat with cream cheese and the remaining raspberry filling.
Frost the top and sides of the cake with the remaining cream cheese frosting.
Garnish with fresh raspberries.