Combine the buttermilk and cold water in a measuring cup, then add the ice cubes. Keep this mixture cold while preparing the dry ingredients so the butter stays firm.

Whisk the flour, chives, sugar, salt, and pepper in a large bowl, then work in the butter with your fingertips. Leave about half the butter in pea-size pieces and flatten the larger pieces into thin shards for flaky pockets.

Discard the ice cubes and add the cold buttermilk mixture to a well in the flour mixture, stirring with a fork until rough clumps form. Stop while a few dry floury spots remain, because the dough will finish coming together during shaping and chilling.

Turn the dough onto a clean surface and press it into a 6-inch square with a bench scraper or straight edge. If it seems unusually crumbly, sprinkle on a little water, using only enough to help the mass hold together.

Cut the square into four pieces, stack them, and press the stack into a mass about 2 inches thick. This stacking creates distinct butter layers that bake into crisp, flaky sheets.

Wrap the dough loosely, roll it into a compact disc about 1 inch thick, and refrigerate for at least 2 hours or up to 2 days. The chilled dough should feel firm and smooth enough to roll without smearing butter.

Lightly tap the chilled dough with a rolling pin if needed, then roll it on a floured surface into a 12-inch round. Roll from the center outward and rotate the dough often to keep the round even.

Set the dough in a 9-inch pie plate, letting it settle into the bottom and sides without pulling or stretching it. Trim the edge to a ½-inch overhang, fold it under to the rim, crimp it, and prick the base and sides with a fork.

Freeze the shaped crust for about 20 minutes until very firm while heating the oven to 425°F. A thoroughly chilled shell holds its shape and keeps the butter from melting too quickly.

Line the cold crust with foil, fill it with pie weights or dried beans, and place it on a rimmed baking sheet. The weights support the sides and prevent the bottom from puffing as the pastry starts to bake.

Bake on the middle rack for 20 minutes, remove the foil and weights carefully, lower the oven to 350°F, and bake for 15 minutes more. The finished shell should be golden brown across the bottom and sides, not merely pale at the edges.

Cool the crust completely in the pan on a wire rack. A cool, fully baked shell gives the tomato filling its best chance of staying crisp underneath.

Set the oven to 375°F and line a rimmed baking sheet with paper towels, then cut the tomatoes into ½-inch slices. Arrange them in one layer, sprinkle with the salt, and let them stand while preparing the custard.

Whisk the buttermilk, mayonnaise, egg, egg yolk, Dijon mustard, black pepper, and cayenne, if using, in a medium bowl. Mix until the custard looks smooth and lightly glossy, then fold in the basil and chives.

Press the tomato slices firmly with fresh paper towels before filling the crust. The surfaces should feel tacky rather than wet, which means much of the loose juice has been removed.

Arrange half the tomatoes in the cooled crust, pour in the herb custard, and scatter the Cheddar evenly over it. Lay the remaining tomato slices on top in overlapping rows and press them down gently.

Place the pie on a rimmed baking sheet and bake on the middle rack for 50 to 60 minutes, rotating it halfway through. The filling should be set in the center, with bubbling golden edges and a deeply browned crust.

Loosely tent the pie with foil if the crust darkens before the filling has finished baking. The foil should shield the rim without touching the cheese-topped surface.

Cool the pie completely for at least 1 hour, then finish with more chopped chives and slice. The rest gives the custard time to firm up, so wedges come out clean instead of collapsing onto the plate.