Preheat oven to 350°F (175°C). Line a 9x13 pan with parchment paper.
Make the crust: In a bowl, combine flour, powdered sugar, and salt. Cut in cold butter until the mixture resembles coarse crumbs. Press evenly into the bottom of the pan.
Bake crust for 18–20 minutes or until lightly golden. Let cool slightly.
Prepare lemon filling: In a separate bowl, whisk eggs, sugar, lemon juice, zest, flour, and salt until smooth.
Strain filling through a fine-mesh sieve to remove lumps.
Add frozen blackberries directly to the filling. Toss fresh berries in flour if using, then fold in.
Pour filling over pre-baked crust.
Reduce oven temp to 325°F (160°C) and bake for 25–30 minutes, or until the edges are set and the center jiggles slightly.
Cool completely, then chill in the fridge for 2–3 hours before slicing.
Dust with powdered sugar and serve.