Proof yeast. Stir yeast into warm milk with a pinch of the sugar. Let stand until foamy, 5–10 minutes.
Whisk flour, remaining dough sugar, and salt in a large bowl.
Mix in eggs, vanilla, and softened butter until shaggy.
Pour in the yeast mixture. Knead by mixer or hand until smooth and elastic, 8–10 minutes.
Let dough rise covered in a greased bowl until doubled, about 60–75 minutes.
Make filling. Combine chopped chocolate, cocoa, brown sugar, cinnamon, and salt. Stir in melted butter to form a spreadable paste.
Roll dough on a lightly floured surface to a 12x16-inch rectangle, long side facing you.
Spread filling evenly, leaving a 1/2-inch border. Roll tightly into a log from the long side.
Chill the log 10 minutes to firm, then slice lengthwise to expose layers.
Twist the two strands, cut sides up. Tuck ends under and place in a lined 9x5-inch loaf pan.
Proof until puffy, 30–40 minutes. Meanwhile, heat oven to 350°F.
Bake until deep golden and set in the center, 33–38 minutes.
Make syrup. Simmer water and sugar 2 minutes. Off heat, stir in vanilla.
Brush hot loaf generously with warm syrup. Cool in pan 15 minutes, then finish on a rack. Slice once warm.