Preheat your oven to 350°F (175°C). Line an 8×8 inch baking pan with parchment paper, leaving an overhang for easy removal.
Prepare the crust: In a medium bowl, whisk together the 1 1/2 cups flour, 1/2 cup sugar, and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.
Mix in the egg yolk and cold water until the dough just comes together. Press this mixture evenly into the bottom of the prepared pan to form the base layer.
Bake the crust for 15 minutes until lightly golden. Remove from the oven.
Prepare the filling: In a separate bowl, gently toss the blueberries with the 2 tablespoons of flour. Set aside.
In another bowl, whisk together the 1/2 cup sugar, lemon juice, lemon zest, and 2 eggs until smooth.
Pour the lemon mixture evenly over the partially baked crust. Sprinkle the floured blueberries over the top of the lemon mixture.
Return the pan to the oven and bake for 25 to 30 minutes, or until the center is mostly set and the edges are lightly browned.
Let the bars cool completely in the pan on a wire rack. This cooling time is important for setting the layers.
Once cool, lift the bars out using the parchment overhang. Dust the top lightly with powdered sugar before cutting into squares.
Notes
If using frozen blueberries, do not thaw them before tossing with the flour.
For a crispier topping, you can reserve 1/4 cup of the crust mixture to sprinkle on top before baking instead of dusting with powdered sugar later.
Allow the bars to chill in the refrigerator for at least one hour before slicing for the cleanest cuts.