To make dough: whisk together flour, cake flour, baking powder, baking soda, and salt. Set aside. In the bowl of a stand mixer fitted with the paddle attachment, cream butter, sugar, and brown sugar. Add the egg and mix until just combined. Scrape bowl as needed.
Add half of dry mixture to creamed butter. With the mixer running, slowly add cream. Add the remaining dry mixture and mix until just incorporated.
Turn dough out onto a clean working surface. Divide dough into two equal parts. Wrap in plastic wrap and chill in the fridge for at least 1 hour (up to overnight).
Filling: While the dough is chilling, make apple cinnamon filling. Place chopped apples, brown sugar, sugar, ground cinnamon, and lemon juice in a medium sauce pot over medium heat. Stir to combine until sugar dissolves. Let simmer until apples are soft and tender, about 10-15 minutes. Strain apples, reserving liquids. Transfer apples to a food processor. Add 1 Tbsp of reserved liquids. Pulse until mixture resembles jam. Add additional reserved liquids (1/2 Tbsp at a time) until mixture resembles thick jam. let cool to room temperature before filling the pop tarts. Alternatively, transfer to an airtight container and let chill in the fridge until ready to use.
Egg Wash: Whisk together egg, water, salt, and cream. Set aside.
Once dough has chilled, remove one piece of dough from fridge. Roll to 1/4-inch thickness on a lightly floured surface. Cut dough into rectangles 3x5 inches in size. Repeat with second dough. Press and knead together scraps and roll dough out again, until you end up with 20 rectangles (10 tops and 10 bottoms).
Spoon a rounded 1 1/2 tablespoons of apple cinnamon filling into the center of 10 rectangles. Spread filling leaving a clean frame around the filling for sealing the edges of the pop tart. Lightly brush egg wash along the clean frame. Place the remaining rectangles over the filled rectangles. Line up the edges of the top and bottom piece, then press the edges to seal. Be careful not to overfill the pop tarts.
Place pop tarts on a parchment lined baking sheet. Freeze pop tarts for at least 1 hour until solid.
Preheat oven to 350 degrees F. Lightly brush the tops of the pop tarts with egg wash. Bake for 10 minutes, rotate pan, and continue baking for another 10 minutes until pop tarts are golden brown in color. Let sit in baking sheet for 3-5 minutes before transferring to a wire rack to cool to room temperature.
To make cinnamon glaze: whisk together confectioners' sugar, vanilla, ground cinnamon, and milk until smooth. Let glaze sit for 5 minutes to slightly thicken. Drizzle glaze over cooled pop tarts. Garnish with sprinkles, if desired. Serve at room temperature or microwave for a couple seconds to warm up.