How to Make It
In a small bowl, combine the water and vinegar and chill the mixture in the freezer until very cold. In a food processor, pulse the flour with the cornmeal, sugar and salt. Add the butter and pulse in 1-second bursts until the mixture resembles coarse meal. Drizzle the vinegar mixture on top. Pulse in 1-second bursts until the dough just comes together. Turn the dough out onto a work surface, gather up any crumbs and pat into a disk. Wrap in plastic and let rest at room temperature for 30 minutes.
On a floured work surface, roll out the dough to an 11-inch round, a scant 1/4 inch thick. Ease the dough into a 9-inch glass or ceramic pie plate. Trim the overhanging dough to 1 inch, fold it under itself and crimp decoratively. Freeze the crust until firm, about 15 minutes.
Preheat the oven to 350°. Line the crust with parchment paper and fill with pie weights or dried beans. Bake in the lower third of the oven for about 20 minutes, until the crust is barely set. Remove the parchment and pie weights. Cover the rim of the crust with strips of foil and bake for about 10 minutes longer, until the crust is lightly browned. Leave the foil strips on and transfer to a rack to cool.
Brush the tomato slices with olive oil and arrange on a rimmed baking sheet. Bake until the tomatoes soften and have released most of their liquid, about 15 minutes. Carefully transfer the tomatoes to a paper towel–lined plate. Peel off and discard the skins.
In a blender, combine the eggs, cream, milk, crème fraîche, onion, hot sauce, sugar and salt and blend until smooth, about 20 seconds. Add the piquillo peppers and cheese and pulse until blended.
Set the pie plate on a baking sheet. Arrange the tomato slices on the bottom of the pie crust and pour in the filling. Bake the pie in the lower third of the oven for 35 to 40 minutes, until the filling is set around the edge but the center is slightly jiggly. Let the pie cool completely before serving.