In a heavy large saucepan combine egg yolks, milk, sugar, stick cinnamon, the 10 coffee beans, and the vanilla bean (if using). Cook and stir over medium heat about 10 minutes or just until mixture coats a metal spoon. Remove from heat. Place the saucepan in a sink or bowl of ice water and stir mixture for 2 minutes. Discard stick cinnamon and remove vanilla bean. Do not remove coffee beans. Using a sharp knife, halve vanilla bean lengthwise; use the tip of the knife to scrape out the seeds. Add seeds to egg yolk mixture; discard vanilla bean pod. Transfer egg yolk mixture to a pitcher.

Stir in rum, Kahlua, and vanilla extract (if using). Cover and chill for 4 to 24 hours before serving. If desired, sprinkle the pitcher or each serving with ground nutmeg and garnish with a few additional coffee beans. (Coffee beans are an edible garnish.)