Place the papaya cubes in a blender, a few at a time; blend until shredded.

Combine 2 cups shredded papaya, white sugar, brown sugar, and salt in a saucepan over medium heat; cook and stir until sugars dissolve, about 5 minutes. Stir cinnamon into papaya mixture and remove saucepan from heat. Drain juice from papaya mixture using a strainer.

Preheat oven to 350 degrees F (175 degrees C). Lightly grease a baking sheet.

Roll pie crusts on a work surface and cut out twenty-four 4-inch circles using a biscuit cutter or a cup. Spoon a small spoonful of papaya mixture into the center of each circle. Fold each circle in half over the papaya, creating a half-circle. Press the edges together using a fork and poke the top for ventilation. Place turnovers 1 inch apart on the prepared baking sheet.

Bake in the preheated oven for 20 minutes. Brush the top of each turnover with egg yolk and continue baking until golden brown, about 15 minutes more.