Break or chop the semisweet chocolate into small, uniform pieces. Microwave in short 20-second bursts, stirring between each, until completely melted and smooth.
Stir the brown sugar, cinnamon, and salt into the melted chocolate. The mixture may look gritty, but this is normal—those sugar crystals will melt beautifully in the oven. Set the filling aside.
Take one dough disk from the fridge and place it on a lightly floured surface. Roll it out into a circle approximately 10 inches in diameter. Spread one-quarter of the chocolate filling evenly over the surface in a thin, consistent layer.
Using a sharp knife or pizza cutter, divide the circle into 16 narrow wedges, like slicing a pizza. Beginning from the wider edge, gently roll each wedge toward the center to form crescent-shaped cookies. Transfer each piece to the prepared baking sheet, spacing them about 2 inches apart. Work swiftly, as the chocolate may begin to firm up. If it does harden slightly, it will still roll and bake beautifully.
Whisk together the egg and water to make an egg wash. Using a pastry brush, lightly coat each piece of rugelach with the wash. Sprinkle the tops with coarse sugar or nonpareil sprinkles if using, which will add a festive look and delightful texture.
Place the baking sheet on the center rack of the oven and bake at 350°F (175°C) for about 25 minutes, or until the cookies are golden brown and slightly crisp.
Allow the rugelach to cool completely on the baking sheet before serving.