Start by making the crust. In a bowl, mix the flour and sugar. Add the butter and blend with a fork or pastry cutter until crumbly.
Press the crust mixture into a parchment-lined 9x9 baking dish, spreading it evenly.
Place the crust in the freezer for 15 minutes.
Preheat the oven to 350°F. Bake the chilled crust for 10 to 15 minutes, until lightly golden.
While the crust cools, mash the raspberries in a bowl until they form a paste.
Add the eggs, sugar, flour, lemon juice, and lemon zest. Whisk until smooth.
Pour the filling over the cooled crust and spread evenly.
Bake for 25 to 30 minutes, until mostly set with a slight jiggle in the center.
Let the bars cool completely, then refrigerate for at least 1 hour before slicing.
Dust with powdered sugar and garnish with fresh raspberries before serving.