1. Make dough: In a food processor, pulse flour, sugar, and salt to combine. Add butter; pulse until mixture resembles coarse meal, with a few pea-size pieces of butter remaining. Sprinkle with 2 tablespoons ice water; pulse until dough is crumbly but holds together when squeezed (if necessary, gradually add up to 2 tablespoons more water). Do not overmix. Flatten dough into a disk; wrap tightly in plastic. Refrigerate until firm, at least 1 hour (and up to 3 days).

2. Make filling: In food processor, combine almonds and sugar; process until finely ground. Add 1 egg, butter, flour, vanilla, and salt; pulse until smooth, and set aside. In a medium bowl, combine figs and lemon juice; set aside.

3. Preheat oven to 350 degrees. On a large lightly floured piece of parchment paper, roll dough to a 14-inch round. Spread almond filling in center, leaving a 2-inch border; top with fig mixture. Fold border over edge of filling, pleating all around; press down gently to seal. In a small bowl, mix remaining egg with 1 teaspoon water; brush dough with egg wash.

4. Lifting edges of parchment, transfer crostata to a rimmed baking sheet. Bake until crust is golden brown, about 1 hour. Let cool on baking sheet at least 30 minutes. To serve, cut crostata into wedges.