Combine the flour and salt in a large bowl, then cut in the cold cubed butter until it looks like coarse crumbs. Slowly add ice water, one tablespoon at a time, until the dough just comes together. Divide it into two discs, wrap in plastic, and chill for at least 30 minutes.
While the dough chills, melt butter in a skillet over medium heat and add the diced apples. Sprinkle in the brown sugar, cinnamon, nutmeg, and cloves, stirring gently. Cook for 4-5 minutes until the apples soften, then stir in cornstarch to thicken the juices before removing from heat to cool.
On a lightly floured surface, roll out each disc of chilled dough to about ¼-inch thickness. Use a knife or pizza cutter to slice the dough into even rectangles, roughly 3x4 inches, so you get matching top and bottom pieces for each tart.
Spoon about 2 tablespoons of the cooled apple filling onto half of the rectangles, leaving a small border around the edges. Top each with a second rectangle, then press the edges firmly with a fork to seal and prevent any filling from leaking out during baking.
Place the assembled pop tarts on a parchment-lined tray and pop them in the freezer for 15 minutes, or the fridge for 30 minutes. This step firms up the butter again, which is what keeps your crust flaky instead of greasy.
Preheat your oven to 375°F. Brush each tart with the beaten egg wash and poke a few small holes on top to let steam escape. Bake for 20-22 minutes, until the crust is golden brown and slightly puffed.
Once the tarts have cooled for about 15 minutes, whisk together powdered sugar, milk, vanilla, and a pinch of cinnamon until smooth. Drizzle or spread the glaze over each tart and let it set for a few minutes before digging in.