Preheat the oven to 350 degrees F. Place a parchment paper on the baking sheets.
Remove the refrigerated pie crusts from the package and set aside.
Mix the brown sugar, cinnamon, and flour in a medium bowl. Melt the butter and pour over the sugar mixture. Add the vanilla. Mix well, using your hands if necessary to blend. Set aside.
Cut out (18) 3 x 5-inch rectangles by rolling each pie crust into a rectangular shape. Place the template next to the edge and top of a crust and cut around it with a knife. Move the template and cut another rectangle. Continue until you have cut as many as you can.
Pull up all of the excess dough around the rectangles. Then, use a knife to lift a corner of a rectangle. Pull up the cutout and place it on the prepared baking sheet. Repeat, moving all the cutouts to the baking sheet. Reroll the leftover dough and cut out additional rectangles. Then, roll out the second crust and repeat until you have cut out all 18 rectangles.
After 9 rectangles are placed (side-by-side) on the baking sheets, add 2 teaspoons of the sugar mixture side-by-side (and lengthwise) to each. Spread the sugar, but keep it in the middle of the rectangles. Divide any leftover mixture between them.
Brush the beaten egg mixture around the edges of each filled cutout. Add the top cutout to each pop tart. Gently press the edges with your fingers to seal. Then, use the tines of a fork to crimp around each pop tart to seal firmly. Use the fork to dock or make several vent holes in the top of each pop tart.
Brush the top of each pop tart with the egg mixture.
Bake for 24 minutes or until the pop tarts are lightly browned. Rotate the baking sheet after 12 minutes. Remove from the oven and let them cool on the baking sheet.