For the crust: Butter a 13-by-9-inch baking dish and set aside. Add the butter and granulated sugar to the bowl of a stand mixer fitted with a paddle attachment and combine until light and fluffy. In a separate bowl, combine the flour and salt and slowly add to the butter mixture until just combined. Pour the dough into the prepared baking dish and press, making sure the dough comes up the sides of the dish around the edges about 1/2 inch. Refrigerate for 30 minutes.
Preheat the oven to 350 degrees F. Bake the dough until lightly browned, 15 to 20 minutes. Cool on a wire rack. (Leave the oven on.)
For the lemon filling: Cut the lemon in half and slice the lemon halves into thin wheels; remove any seeds. Toss the lemon wheels (with flesh and peel), granulated sugar and chunks of butter into the bowl of a food processor. Process, scraping down the sides as needed, until the lemon is thoroughly pureed. Add the eggs, cornstarch and salt and pulse until the batter is smooth. Pour into the prepared crust.
Bake until the filling is set, 35 to 40 minutes. You can test this by bumping the pan a little; it should only jiggle slightly. In my oven, I find that the point at which the filling is set is also when it starts to get very light brown on top.
Let cool on a rack. Cut into rectangles and dust with powdered sugar.