Preheat oven to 350°F and adjust rack to the middle position. Line a 9-inch square pan with a foil sling and grease the foil.
In a food processor, pulse flour, sugar, and salt. Add butter and pulse until the mixture resembles coarse meal.
Press into the prepared pan and bake until lightly browned, about 20 minutes, rotating halfway. Keep crust hot.
While crust bakes, whisk eggs and yolks in a saucepan. Add sugar, lemon zest, lemon juice, and salt. Stir in butter and cook over medium-low, stirring constantly, until thickened and reaches 170°F.
Strain lemon mixture into a bowl, stir in cream, and pour over the hot crust.
Bake until the filling is just set with a slight jiggle, about 10–15 minutes, rotating halfway.
Cool in pan for 2 hours. Lift out using foil, cut into 16 squares, and dust with powdered sugar before serving.
Store in the fridge for up to 2 days.