In a large mixing bowl, whisk together the flour, sugar, and salt.

Using the large holes of a box grater, grate the very cold butter directly into the flour mixture. Gently toss everything together until the butter is evenly coated.

Add the sourdough discard and ¼ cup cold water. Stir until the dough begins to come together. If needed, add additional cold water, 1 tablespoon at a time, until a shaggy dough forms.

Turn the dough onto a lightly floured surface and gently knead just until it comes together. Shape the dough into a disc, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.

In a small bowl, whisk together the egg and the heavy cream (or milk). Set aside.

Preheat the oven to 350°F (177°C). Line a large baking sheet with parchment paper.

On one half of each rectangle, sprinkle a layer of shredded mozzarella cheese. Top with pepperoni slices, spoon on about 1 tablespoon of marinara sauce, then sprinkle a little more mozzarella over the sauce. This helps keep the sauce from soaking into the pastry and creates an extra cheesy filling.

Brush the edges with the egg wash. Fold the dough over the filling and press the edges together firmly. Crimp with a fork to completely seal each hot pocket.

Transfer to the prepared baking sheet.

Place the baking sheet in the freezer for 20 minutes. This helps keep the butter cold, resulting in a flakier crust while preventing the hot pockets from spreading.

Remove the hot pockets from the freezer.

Brush the tops generously with the egg wash.

Using a sharp knife, cut three diagonal slits across the top of each hot pocket to allow steam to escape.

Sprinkle the tops with grated Parmesan cheese and dried parsley.

Bake for about 30 minutes, or until the pastry is golden brown and crisp.

While still warm, brush each hot pocket with the melted salted butter. Finish with another generous sprinkle of grated Parmesan cheese and a little more dried parsley.

Serve warm with extra marinara sauce for dipping.