Lemon Bars for a Crowd

Preheat oven to 350°. Using an electric mixer on low speed, beat butter, sugar, and salt in a medium bowl until butter is almost completely smooth, about 2 minutes. Increase speed to medium and beat until butter is creamy, about 2 minutes more. Beat in egg yolks and vanilla. Reduce speed to low, add flour, and beat until no dry spots remain.

Firmly press dough into the bottom and ½" up the sides of a 13x9" baking dish (the firmer you press, the easier it will be to cut the crust). Bake crust until golden brown on the bottom and a shade or two darker at the edges, 25-35 minutes. Remove dish from oven and reduce oven to 300°.

Combine lemon juice, salt, and ½ cup sugar in a small saucepan. Scrape in seeds from vanilla bean and add pod. Bring to a simmer over medium heat, stirring to dissolve sugar.

Meanwhile, whisk egg yolks, eggs, and remaining 1 cup sugar in a medium bowl until no longer grainy and slightly lightened in color, about 2 minutes.

Whisking constantly, gradually stream hot lemon mixture into egg mixture, then transfer mixture back to saucepan. Cook over medium heat, whisking constantly, until thickened and marks from whisk are just visible, 5–7 minutes. Remove from heat and whisk in butter, adding a couple of pieces at a time and whisking until incorporated before adding more, until smooth.

Strain warm curd through a fine-mesh sieve into warm crust and bake until curd is set around the edges (filling should still wobble when dish is jiggled; it will set completely as it cools), 15–20 minutes. Do not overbake or filling may curdle. Transfer to a wire rack and let cool, about 2 hours, then chill until cold, at least 1 hour.

Just before serving, cut lemon bars into thirty-two 1½" squares and dust with powdered sugar.

Do Ahead: Lemon bars (without powdered sugar) can be made 3 days ahead. Cover and keep chilled.