Prepare the Shortbread Crust:

1. Preheat the oven to 350°F.
2. In a mixing bowl, add the flour and sugar. Whisk together with a fork. Then add the cubed, softened butter and blend together with a fork or pastry cutter until the mixture is slightly crumbly.
3. Transfer the mixture into a square baking dish lined with parchment paper. Press the mixture into the pan, spreading evenly.
4. Then, place the crust in the freezer for 15 minutes.
5. Once the crust has chilled, bake in the oven for 15 minutes, until lightly browned. Let it cool and set aside.

To Make the Filling:

1. In a mixing bowl, add the rinsed raspberries. Mash them with a fork until a raspberry paste has formed.
2. Add the eggs, sugar, flour, lemon juice, and lemon zest to the raspberry paste. Whisk together for about a minute until the mixture is thoroughly combined.

Bake and Serve Raspberry Lemon Bars:

1. Pour the raspberry lemon mixture on top of the cooled shortbread crust and spread evenly.
2. Bake in the oven for another 30 minutes or until the top is almost completely set and the bars are slightly jiggly. Remove from the oven and let cool completely.
3. Refrigerate the bars, covered, for at least an hour to chill. Dust with powdered sugar before serving.