Wash, dry, peel, and pit the peaches, then dice into small cubes. Toss gently with the granulated sugar in a medium bowl. Cover and refrigerate 1 hour to draw out the juice.
Drain the juice into a heavy-bottomed saucepan, reserving the fruit. Whisk in the cornstarch, cinnamon, and salt until smooth.
Cook over medium-low heat, stirring constantly, until simmering. Continue 2 to 3 minutes until thickened to a syrup. Remove from heat and stir in the lemon juice, almond extract, and vanilla. Fold in the reserved peaches and let cool completely.
Preheat the air fryer to 350°F on the air fry setting. Lightly spray the basket or tray with oil.
Unroll the pie crust on a lightly floured surface. Cut once horizontally and once vertically to make four equal sections.
Brush each section generously with egg wash. Spoon 1 to 1½ tablespoons of cooled filling onto one half, leaving a clear border.
Fold each section over to form a pocket and press the edges firmly with a fork to seal. Cut two small vents in each top.
Brush the tops with egg wash and arrange in the basket in a single layer with space between. Air fry 10 to 15 minutes, turning halfway, until deep golden brown.
Sprinkle with turbinado sugar and rest 5 minutes before serving.