In a 5- to 6-quart pan over medium heat, stir almonds until golden, 5 to 7 minutes.
Add milk and chocolate to pan and stir occasionally over medium heat just until chocolate is melted (flecks are okay) and milk is hot (do not boil), 12 to 15 minutes. Add sugar, vanilla, and ground cinnamon; stir just until sugar is dissolved, about 1 minute.
Pour about a third of the hot milk mixture into a blender. Holding lid down with a towel, whirl until very smooth and frothy; pour into a pitcher. Repeat twice to purée remaining mixture. To serve, pour hot chocolate into cups (8 to 12 oz.) and garnish with cinnamon sticks.