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To make the crust: In the bowl of a food processor, pulse the flour and salt to combine. Don’t have a food processor? See “tips,” below.
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Add the butter cubes and pulse until the pieces of butter are the size of small peas.
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Pour in the ice water and pulse until the dough comes together in a shaggy ball.
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Turn the dough onto a piece of plastic wrap, flatten it with the heel of your hand into a 1"-thick disk, and wrap tightly. Refrigerate for at least one hour, or for up to three days.
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Preheat the oven to 350°F.
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Place the chilled dough on a lightly floured surface and roll it into a 14" round. Transfer it to a deep-dish pie pan (at least 1 1/2” deep), or a high-sided 10" round or 11” x 7” rectangular removable-bottom tart pan, fitting the dough into the bottom and along the sides of the pan.
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Refrigerate the crust for 10 minutes.
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Remove the pan from the refrigerator. Use a fork to prick the bottom ("dock") of the dough all over, then place a 14" sheet of parchment or aluminum foil into the pan. Add enough dried beans, pie weights, or granulated sugar (bonus: it makes toasted sugar) to weigh the paper down, and place the pan on a rimmed baking sheet.
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Bake until the edges of the crust are firm and beginning to turn golden, about 20 to 25 minutes.
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Remove the crust from the oven and carefully remove the weights and parchment or aluminum foil. Return the pan to the oven’s bottom rack and continue to bake until the crust is golden, about 20 to 25 minutes longer.
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To make the filling: In a large bowl, whisk together the mayonnaise, buttermilk, eggs, 1/2 cup (33g) of the grated Parmesan, and the scallions and pepper.
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Pour three-quarters ((about 412g) of the filling into the parbaked crust. Arrange the tomato slices (and cherry tomatoes, if using) in a circular pattern on top, overlapping them slightly and saving a few slices for a garnish. Roughly tear the basil leaves with your fingers and distribute evenly over the tomatoes.
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Pour the remaining custard over the basil, sprinkle with the remaining 1/4 cup (17g) Parmesan, and garnish with the reserved tomato.
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Bake the pie until the crust is a deep golden brown and the filling is set and beginning to brown on top, about 45 to 55 minutes. If the edges brown too quickly, add a crust shield, or cover with strips of aluminum foil.
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Remove the pie from the oven and transfer it to a cooling rack. Let cool for at least 30 minutes. Serve warm or at room temperature.
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Storage information: Store leftover pie, covered, in the refrigerator for several days; freeze for longer storage.