Roll pie crust out, on a very lightly floured surface, into a 12-inch circle. Fit pie crust in an 8-inch metal pie plate. Fold edges under, and decoratively crimp or pinch the edges. Chill until crust is firm, at least 1 hour.
Arrange the oven rack on the bottom positions. Preheat oven to 450ºF (232ºC).
Line pie crust with aluminum foil or parchment paper. Fill (to the top of the crust) with dried beans, pie weights, or a combination of both. Bake at 450ºF (232ºC) for 10-12 minutes, or until the edges are golden. The bottom of the crust will be slightly underbaked. Cool completely on a wire baking rack with pie weights in the shell for about 20 minutes. When cool, remove pie weights and parchment paper.
Reduce oven temperature to 350ºF (177ºC) and move the oven rack up to the middle position.
Fit the top of the crust with a pie shield. Arrange figs in an even layer in the cooled pie crust.
In a large mixing bowl, add eggs (4), sugar (3/4 cup), flour (1/4 cup), butter (1/4 cup), lemon juice (2 tablespoons), and ginger (2 teaspoons). Stir vigorously until well combined. Pour into crust over figs. Place the pie plate on a rimmed baking sheet.
Bake in 350ºF (177ºC) oven until custard is set, 65-72 minutes. Check the pockets of custard on top of the pie, between the figs, for the doneness of the custard. They will be set when the pie is done.