Prepare the crust: Combine the vinegar with 1/2 cup ice water in a small bowl.
Pulse the flour, salt and sugar in a food processor until combined. Add the 4 tablespoons chilled butter and pulse until the butter is in pea-sized clumps and the mixture is sandy. Add the 3 tablespoons frozen butter; pulse until the frozen butter is also in pea-sized clumps. Add 5 tablespoons of the vinegar mixture; pulse 2 or 3 more times. Squeeze a small amount of dough between your fingers. If it does not stay together easily, add 1 more tablespoon of the vinegar mixture and pulse 3 or 4 more times. (Do not let the dough come together.) Turn the dough out onto a clean surface and gather into a lumpy ball; flatten into a disk, wrap in plastic and refrigerate at least 1 hour or overnight.
On a floured surface, roll the dough into a 12-inch circle, about -inch thick. Fit into an 8-inch pie plate and trim the extra dough, leaving a 1-inch overhang; reserve trimmings. Fold the edges under the rim and crimp. Refrigerate the crust until firm, 20 minutes. Meanwhile, preheat the oven to 400 degrees.
Line the chilled crust with foil and fill with pie weights or dry beans. Bake until the edges are golden, 15 minutes. Remove the foil and weights; continue baking until the center of the crust is dry and golden brown, about 12 minutes. Cool slightly on a wire rack. Cover any cracks in the crust with the dough trimmings before filling.
Prepare the filling: Whisk the sugars and the flour in a medium bowl, breaking up any clumps of brown sugar. Combine the heavy cream and vanilla in a separate bowl and slowly whisk into the sugar mixture until smooth. Pour the filling into the prepared crust; bake until the pie begins to set around the edge but is still slightly wobbly in the middle, 40 minutes. (Tent loosely with foil for the last 10 minutes if the crust gets too dark.) Cool to room temperature on a wire rack, then refrigerate until ready to serve. Dust with confectioners' sugar before slicing.
Photograph by Tim Klein
Recipe courtesy Hoosier Mama Pie Company, Chicago, for Food Network Magazine