Wash mint. Remove about a dozen leaves and reserve for garnish. Combine 2 cups of milk, coffee, washed mint stalks and leaves, and cinnamon sticks or powdered cinnamon in a small saucepan or microwave bowl or cup.
Heat over a medium flame or in microwave just until the liquid starts to steam and a few bubbles appear; don't let it boil. Set aside and let steep for at least fifteen minutes and as long as an hour.
For foamed milk, place 1 cup of hot milk in a blender container with the sugar. Cover with a vented lid. Blend until frothy, about 30 seconds. Switch the blender on and off quickly to avoid splashing overflows, and then continue blending.
Pour coffee-mint mixture through a clean strainer into a pitcher or large measuring cup; if it has cooled, reheat without letting it come to a boil. Stir in the optional mint syrup or creme de menthe.
Divide coffee among three serving cups and spread foamed milk over each one. Sprinkle four or five red-hots over foamed milk and garnish with two or three mint leaves.