Preheat oven to 325 degrees. Line a 9-by-9-inch baking pan with parchment paper.
STEP 2
For the crust, pulse flour, granulated sugar, confectioners’ sugar, lemon zest, and salt in a food processor. Add butter and pulse until crumbly. Press dough into the pan and bake until golden, about 30 to 35 minutes.
STEP 3
While crust bakes, prepare lemon curd: Grate zest from lemons and set aside. Juice lemons to get 3/4 cup.
STEP 4
In a small saucepan, whisk lemon juice, sugar, eggs, yolks, cornstarch, and salt. Heat over medium until boiling and thickened, about 2 to 5 minutes. Remove from heat and strain into a bowl. Whisk in butter, olive oil, and lemon zest.
STEP 5
Pour lemon curd over the baked crust. Bake until set, about 10 to 15 minutes. Cool to room temperature, then chill before cutting. Dust with confectioners’ sugar and sea salt before serving.