To make the crust, butter a 9-by-13-inch baking pan or glass baking dish. In a food processor, process the pistachios and lemon zest until finely chopped, about 30 seconds. Add the flour, sugar and salt; process until well combined, 10 to 20 seconds. Scrape the bowl and pulse a few times to ensure no dry, floury patches remain. Scatter the butter over the mixture and drizzle in the oil, then process until large, evenly moistened clumps form, 45 to 60 seconds.
Crumble the dough clumps into the prepared pan, evenly scattering the bits. Using your fingers, press into an even layer. Lightly brush with the beaten egg white and refrigerate, uncovered, until cold and firm, about 30 minutes. Meanwhile, heat the oven to 350°F with a rack in the middle position.
Bake the crust until golden brown, 22 to 26 minutes. While the crust bakes, make the filling. In a large bowl, combine the whole eggs and yolks, sugar and lemon zest; whisk gently just until smooth (avoid aerating the mixture). Add the flour and salt; stir with a silicone spatula until combined. Stir in the lemon juice, cream and oil.
When the crust is done, remove the pan from the oven. Gently stir the filling to recombine, then pour it onto the hot crust; if any large bubbles rise to the surface, pop them with a toothpick or skewer. Return to the oven and bake until the filling is set, 24 to 27 minutes. Cool completely in the pan on a wire rack, about 3 hours.
Using a sharp knife, cut the bars in the pan lengthwise into quarters, then crosswise into sixths, creating 24 squares. Remove from the pan with an offset spatula. Dust with powdered sugar just before serving.
Lemon Bars with Pistachios and Lavender: Follow the recipe to make the crust, adding ¾ teaspoon dried lavender to the food processor with the pistachios and lemon zest. Make and slice the bars as directed. After dusting with powdered sugar, sprinkle additional lavender (lightly crushed) over the bars.
Lime Bars with Coconut and Cashews: Follow the recipe to make the crust, replacing the pistachios with (¾ cup) roasted, unsalted cashews and (¼ cup) unsweetened shredded coconut and replacing the lemon zest with an equal amount of lime zest. Press the dough into the pan, chill and bake the crust as directed. While the crust is baking, make the filling, substituting an equal amount of lime zest and juice for the lemon zest and juice. When the crust is done, remove the pan from the oven. Gently stir the filling to recombine, then pour it onto the hot crust. Bake, cool and cut as directed, dusting the bars with powdered sugar and additional grated lime zest just before serving.
Citrus Bars with Thyme and Hazelnuts: Follow the recipe to make the crust, replacing the pistachios with 1 cup roasted, unsalted hazelnuts, replacing the lemon zest with an equal amount of orange zest and also adding 2 teaspoons fresh thyme. Press the dough into the pan, chill and bake the crust as directed. While the crust is baking, make the filling, replacing the lemon zest with an equal amount of orange zest and replace the lemon juice with ¾ cup grapefruit juice plus ¼ cup orange juice. When the crust is done, remove the pan from the oven. Gently stir the filling to recombine, then pour it onto the hot crust. Bake, cool and cut as directed, dusting the bars with powdered sugar and flaky sea salt, if desired, just before serving.