Whisk the flour and 1/4 tsp salt together in a mixing bowl. Add the cold cubed butter and cut it in with a pastry cutter or your fingers until the mixture looks like coarse crumbs with pea-sized bits of butter.

Sprinkle in the ice water one tablespoon at a time, mixing gently with a fork, until the dough just clumps together when pressed. Shape into a disk, wrap, and chill for 30 minutes.

Roll the chilled dough on a floured surface into a 30 cm / 12-inch circle. Fit it into a 23 cm / 9-inch pie dish, trim the overhang to 2 cm / 3/4 inch, and crimp the edges. Chill the crust while you make the filling.

Heat the oven to 190 C / 375 F.

Combine the brown sugar, heavy cream, and 45 g butter in a 2-quart / 1.9 L saucepan over medium heat. Whisk constantly for 3 to 4 minutes until the sugar dissolves and the mixture is smooth, without letting it come to a hard boil.

Remove from the heat and let cool for 5 minutes. Whisk in the flour until no lumps remain.

Whisk in the egg, vanilla, and pinch of salt until fully blended and glossy.

Pour the filling into the chilled crust.

Bake for 10 minutes at 190 C / 375 F, then lower the oven to 160 C / 325 F and continue baking for 30 to 35 minutes, until the edges are puffed and set and the center still jiggles slightly like loose gelatin, similar to a pecan pie. An instant-read thermometer inserted in the center should read about 175 F / 79 C.

Cool the pie on a wire rack for at least 2 hours at room temperature before slicing. It looks underdone warm but firms up completely as it cools, and cutting into it early is the main reason sugar pie turns runny.

Slice into 8 wedges and serve at room temperature or slightly warm.