In a medium bowl, lightly beat the eggs. In a small saucepan, heat the milk and the sugar over medium-low heat until almost simmering. Remove from the heat and slowly whisk the hot milk into the eggs. Pour the custard into the saucepan and cook over low heat, stirring constantly with a wooden spoon, until the custard begins to thicken, about 3 minutes. Strain the custard mixture into a medium heatproof bowl, then transfer to ramekins or 4 small heatproof mugs. Place 1 cinnamon stick in each custard.
Add the apple cider and the remaining cinnamon stick in the steamer base and bring to a simmer. Set the ramekins in the steamer basket, cover and cook until loosely set, about 10 minutes. Turn off the heat and let sit, covered, for 5 minutes. Remove the custards from the steamer basket and refrigerate until set, about 1 hour.
Meanwhile, pour the cider into a medium saucepan. Simmer over medium-high heat, stirring occasionally, until reduced to 1/3 cup, about 15 minutes. Remove the cinnamon stick and let cool. Drizzle the chilled custards with the cider syrup.