Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the sifted flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
With the mixer on low speed, alternately add the flour mixture and the milk to the butter mixture, beginning and ending with the flour mixture. Mix just until combined.
Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula.
Bake for 28-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes, then turn out onto wire racks to cool completely.
While the cakes are cooling, prepare the raspberry filling. In a small saucepan, combine the fresh raspberries, granulated sugar, and lemon juice.
Cook over medium heat, stirring occasionally, until the raspberries release their juices and the mixture begins to simmer, about 5 minutes.
In a small bowl, mix the cornstarch and cold water until smooth. Stir the cornstarch mixture into the raspberry mixture.
Continue cooking and stirring until the filling thickens, about 2 minutes. Remove from heat and let cool to room temperature.
Once the cakes and raspberry filling are completely cool, place one cake layer on a serving plate.
Spread the raspberry filling evenly over the top of the first cake layer.
Place the second cake layer on top of the filling and gently press down.
Optional: frost the cake with your favorite vanilla buttercream or whipped cream, or serve as is.