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 1 3/4 cups sugar 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 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.
Bake for 28-30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and let them cool in the pans for 10 minutes. Then, turn them out onto wire racks to cool completely.
While the cakes are cooling, prepare the raspberry filling. In a small saucepan, combine the raspberries, 1/4 cup sugar, and lemon juice. Cook over medium heat, stirring occasionally, until the raspberries release their juice and the mixture begins to simmer, about 5 minutes.
In a small bowl, mix the cornstarch and water until smooth. Stir this mixture into the raspberry sauce and cook for another 1-2 minutes until thickened.
Remove the raspberry filling from heat and let it cool completely to room temperature.
Once the cakes are completely cool, place one cake layer on a serving plate. Spread the raspberry filling evenly over the top.
Place the second cake layer on top of the filling. Optionally, dust the top with powdered sugar or frost as desired.
Slice and serve.