Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.

Roll pie crust out on a floured work surface to about 10 inches. Transfer to the prepared baking sheet.

Combine blueberries, flour, sugar, tarragon, lemon zest and juice, and almond extract in a medium bowl. Mix well.

Spoon blueberry mixture into the center of the pie crust, leaving about a 2-inch border. Place fig slices in the center in a circular pattern. Fold crust up all around the edge of the blueberries, crimping and pinching to create pleats.

Whisk egg and water together in a small bowl. Brush edges of crust with mixture and sprinkle with turbinado sugar.

Bake in the preheated oven until crust is crispy and golden brown, about 20 minutes. Remove from the oven and set aside to cool and set, 15 to 30 minutes. Serve warm or at room temperature.