In a small bowl, combine warm milk, yeast, and 1 tablespoon of the granulated sugar. Let it sit for 5-10 minutes until foamy.
In a large bowl, whisk together the remaining granulated sugar, egg, and melted butter. Stir in the yeast mixture.
In a separate bowl, whisk together the flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms.
Turn the dough out onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic. Place the dough in a greased bowl, cover, and let rise in a warm place for 1-1.5 hours, or until doubled in size.
While the dough is rising, prepare the filling. In a medium bowl, mix softened butter, brown sugar, cocoa powder, and cinnamon until well combined.
Punch down the risen dough and turn it out onto a lightly floured surface. Roll the dough into a large rectangle, about 12x18 inches.
Spread the chocolate filling evenly over the dough, leaving a small border.
Starting from the long edge, tightly roll up the dough. Pinch the seam to seal.
Cut the roll into 12 equal slices. Place the slices, cut-side up, in a greased 9x13 inch baking pan.
Cover the pan and let the rolls rise for another 30-45 minutes.
Preheat oven to 375 degrees F (190 degrees C). Bake for 20-25 minutes, or until golden brown.
While the rolls are baking, prepare the glaze. In a bowl, whisk together powdered sugar, melted butter, milk, and vanilla extract until smooth and creamy.
Let the rolls cool slightly before drizzling with the glaze.
Notes
These chocolate cinnamon rolls are best enjoyed warm. You can also add a pinch of salt to the glaze for a salted caramel effect.