Place all ingredients, except the cinnamon reserved for garnish and rum (if using), in a medium pot and bring to a simmer over medium-high heat.

Reduce to heat to low, and let mixture steep for at least 30 minutes, stirring occasionally. Remove ginger root and discard.

Using an immersion blender, purée mixture until very smooth.

(Note: if you are using a regular blender, let mixture cool a bit before blending.)

Pour mixture through a fine-mesh strainer into a heatsafe bowl, discard solids and repeat process, pouring contents once more through strainer back into pot.

If you're adding rum, add preferred amount to the pot and keep warm on the stove until ready to serve.

Divide "eggnog" into cups and garnish with ground cinnamon.