In the bowl of a stand mixer fitted with the paddle attachment, combine 1½ cups (188g) flour, ¼ cup (50g) sugar, yeast, and 1½ teaspoons (4.5g) salt.
In a medium saucepan, heat water, milk, and ⅓ cup (76g) butter over medium heat until an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm milk mixture to flour mixture, and beat at medium speed until combined. Add egg, beating until combined. With mixer on low speed, gradually add 2 cups (250g) flour, beating just until combined and stopping to scrape sides of bowl.
Switch to the dough hook attachment. Beat at low speed until a soft, smooth, and somewhat sticky dough forms and pulls away from sides of bowl, 8 to 9 minutes. Add up to remaining ¼ cup (31g) flour, if necessary. Turn out onto a lightly floured surface, and shape into a smooth round.
Lightly spray a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 40 minutes to 1 hour.
Spray a 10-inch cast-iron skillet with cooking spray.
In a small bowl, whisk together cocoa, cinnamon, remaining ⅓ cup (76g) butter, remaining ¼ cup (50g) sugar, and remaining ½ teaspoon (1.5g) salt.
Lightly punch down dough. Cover and let stand for 5 minutes. Turn out dough onto a lightly floured surface, and roll into an 18x12-inch rectangle. Spread cocoa mixture onto dough, leaving a ½-inch border on one long side. Sprinkle with chopped chocolate. Starting with opposite long side, roll up dough, jelly roll style; pinch seam to seal. Gently shape log to 18 inches long and even thickness, if necessary. Using a serrated knife dipped in flour, cut log into 12 slices (about 1½ inches thick). Place slices, cut side down, in prepared skillet. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed, 20 to 30 minutes.
Preheat oven to 350°F (180°C).
Bake until lightly golden and an instant-read thermometer inserted in center registers 190°F (88°C), 35 to 40 minutes, loosely covering with foil to prevent excess browning, if necessary. Let cool in skillet for 10 minutes.
Make the cream cheese glaze: In a medium bowl, whisk cream cheese until smooth. Whisk in confectioners’ sugar. Add milk, 1 tablespoon (15g) at a time, until fluid.
Top rolls with Cream Cheese Glaze; garnish with cinnamon, if desired. Serve warm or at room temperature.