Melt chocolate and butter together in short microwave intervals, stirring until smooth. Mix in cocoa powder and sugar; set aside at room temperature until spreadable.

Divide dough in half, then divide each half again. Roll each piece into a thin rectangle, spread evenly with filling, and roll tightly from the short side into logs. Twist two logs together, place in a parchment-lined loaf pan, and repeat with remaining dough. Cover and let rise until slightly puffed, about 30 minutes.

Heat oven to 350°F/175°C. Brush loaves with egg and bake until deeply golden, 40 to 45 minutes.

While baking, boil sugar and water for 2 minutes, then cool. Brush hot loaves generously with syrup. Cool briefly in pans, then transfer to a rack.