In large saucepan, combine water, honey, vanilla, cinnamon, plus annatto and chile (if using). Bring to boil over medium-high heat. Remove from heat, add the chocolate, and stir until melted and thoroughly combined.
Return pan to heat and bring mixture to rolling boil (if using milk, bring to just below boiling point). Remove pan from heat for a moment, then return to heat and bring to boil (or almost a boil) a third time. Remove from heat and beat with a whisk or rotary beater until frothy on top.
Pour 3/4 of chocolate into 4 cups. Beat remaining chocolate in saucepan until thick froth forms. Spoon froth on top of chocolate in cups.