For the lemon cream filling:
For the dough:
To make the lemon cream, combine the sugar and lemon zest in a heatproof bowl. Mix together with your fingertips until the mixture resembles wet sand. Whisk in the eggs until the mixture is slightly thickened, about 1 minute. Whisk in the lemon juice.
Place the bowl over a pot of simmering water to form a double boiler. Let the mixture cook, stirring frequently, until the cream thickens (around 175-180˚ F on an instant read thermometer). Remove the bowl from the heat and let cool to 140˚ F (about 10-15 minutes). Once the mixture has cooled, add in the butter a few pieces at a time and whip on medium speed with a hand mixer (or in the bowl of a stand mixer fitted with the whisk attachment) until the mixture is thick and pale, about 3-4 minutes total.
Preheat the oven to 350˚ F. Line an 8 x 8-inch baking pan with foil. In a medium bowl, combine the sugar, baking powder, flour, and salt, and stir together with a fork. Cut in the butter and egg with a pastry blender until the largest chunks are about pea-sized. The mixture should be crumbly without much loose flour.
Spread about half of the dough mixture in an even layer over the bottom of the prepared pan and press down firmly to form the bottom crust. Pour the lemon cream filling over the crust and spread in an even layer. Crumble the remaining dough over the top of the lemon cream.
Bake for about 35-40 minutes, or until the top is slightly browned and the center is just set. Remove to a wire rack and let cool to room temperature. Cover and refrigerate until thoroughly chilled. Slice and serve, dusting with confectioners’ sugar if desired.