In the bowl of a food processor, add flour, sugar, salt and cinnamon. Add butter and process for approximately 10 seconds, or just until the mixture resembles a coarse meal.
With the machine running, add ice water, drop by drop and slowly add egg yolks, until the dough just holds together without being wet or sticky; about 30 seconds. Test the dough at this point by squeezing a small amount together. If it is too crumbly, add a bit more water.
Turn dough out onto a large piece of plastic wrap. Grasping the ends of the plastic wrap with your hands, press dough into a flat circle with your fists. Wrap dough in the plastic and chill for at least an hour.
Line a baking sheet with parchment paper. Sprinkle a lightly floured work surface with turbinado sugar. Roll out dough to about 1/4-inch thickness and with cut out circles 4 ½ inches in diameter. Combine leftover dough scraps and repeat, until you have about 14 circles.
In a small bowl, mix together 2 tablespoons flour, granulated sugar, cinnamon, nutmeg and ginger; set aside.
In a large bowl toss together plums and lemon zest. Sprinkle the flour mixture over plums; gently toss until evenly coated.
Evenly transfer the plum mixture into the middle of each dough circle, leaving a 1-inch border all the way around. Fold border over plum mixture, overlapping where necessary and gently pressing to adhere the folds. Transfer to the prepared baking sheet. Dot plums with butter and place in freezer for 15 minutes until firm. Preheat oven to 375 degrees.
In a small bowl, beat together egg with 1 teaspoon water. Brush edges of dough with egg mixture, and sprinkle with turbinado sugar.
Bake until crust is golden brown and juices are bubbling, about 30 minutes. Transfer the baking sheet to a wire rack to cool. Serve warm or at room temperature.