Pour 5 1/2 cups milk into a large, heavy-bottomed saucepan.
In a small bowl, combine the cornstarch, cocoa powder, sugar, and salt. Add the remaining 1/2 cup milk to form a smooth paste.
Heat the milk over medium heat and add cocoa mixture just before the milk boils.
Allow to boil, stirring constantly for one minute or until slightly thickened.
Remove from heat and stir in vanilla and 8 ounces of the chocolate. Stir until chocolate is completely melted and combined. Add more chocolate, little by little, to taste.
Set aside and keep warm.
Start the churros.
Combine the water, olive oil, and salt in a medium heavy-bottomed non-aluminum saucepan. Bring to a rolling boil over high heat. Remove from heat and add all the flour. Stir briskly with a wooden spoon until the dough gathers in a clump around the spoon and pulls away from the sides of the pan.
Place the pan over medium heat and stir the batter briskly for 30-60 seconds more to dry out any excess moisture and eliminate raw flour taste.
Turn the dough out onto an aluminum foil-lined work area.
Pat the dough into an 8 inch circle and let cool for 5 minutes. Return the dough to the pan.
One at a time, beat the eggs into the dough, stirring briskly after each addition just until the egg is fully incorporated and the dough is smooth.
The dough should end up smooth, slightly sticky, and malleable, but firm enough to form soft peaks and hold its shape when piped or scooped.
Pour 3 inches of oil into a heavy pan or deep fryer. Heat the oil to 365°F.
Meanwhile, stir the sugar and cinnamon together in a large, shallow dish.
Put a large, star-shaped pastry tip into a pastry bag and pipe strips or coils of dough into the hot oil.
Fry one large spiral or 4 strips at a time.
Fry until golden brown, using tongs to turn the pastries about 2 minutes per side.
Use a wire-mesh skimmer to transfer the hot churros to a paper towel-lined plate to drain.
While still warm, roll the churros in the cinnamon-sugar.
Place churros on a baking sheet and keep warm at 200°F in an oven.
Betwen each batch of churros, allow the oil to return to 365°F
When all the churros are finished, gently rewarm hot chocolate if necessary.
Pour the hot chocolate into six 1-cup bowls or cups and top each with a dollop of whipped cream. Serve with churros for dipping.