Preheat the oven to 425 degrees F. Let the dough soften at room temperature for 10 minutes. Line a baking sheet with parchment paper. Lay the pie crust on the parchment paper. Spread the fig jam on the crust, leaving a 2-inch clean border around the edge. Arrange the plums on top of the jam. Fold the crust's edge inward, pleating as needed; leave the center of the tart exposed. Press the dough lightly to seal.
Whisk the egg with 1 tablespoon water in a small bowl; brush the egg wash on the dough and sprinkle with the sugar. Bake until the crust is cooked through and golden brown, about 35 minutes. Serve warm with ice cream, if desired.