In the bowl of a food processor, pulse together the all-purpose flour, powdered sugar, and salt until combined. Add the butter and pulse in short bursts until the butter is the size of small peas. Slowly add the beaten egg and pulse until the mixture comes together into a ball. Shape into a disk, wrap in plastic wrap and chill for at least 2 hours.
Let the dough sit at room temperature for a few minutes, then roll out into a rough 13-inch circle. Transfer the dough to an 8 or 9-inch greased tart pan with removable sides. Freeze for at least 30 minutes before baking.
Preheat oven to 375°F. Place the tart on a sheet pan and cover with a greased sheet of foil, shiny side down. Fill tart with dried beans or pastry weights and bake for 25 minutes. Remove foil and bake uncovered for another 5 minutes.
To make the filling:
In the bowl of a food processor, pulse the lemon slices, sugar, and sugar until pureed. Add the eggs, cornstarch, and salt and pulse until smooth. Pour into the parbaked shell and bake until the middle is set, or just barely jiggles when bumped, 25 minutes.
Let cool slightly before removing sides. Serve warm or chilled. Store tart in the fridge.