In a medium saucepan, bring the sugar, water, cinnamon stick, and lemon zest to a simmer over medium heat.
In a large bowl, beat together the egg and egg yolks until smooth.
Once the sugar has dissolved, remove and discard the cinnamon stick and lemon.
Reduce the heat to a low simmer. Hold a fine mesh sieve over the pot of syrup and slowly pour the egg mixture into the sieve in a circular motion over the pot to form thin strands.
Cook the mixture, stirring with a wooden spoon and scraping along the bottom and edges to prevent a crust from forming, until the eggs are cooked through and only a little syrup remains.
Transfer the mixture to a 5-6 inch (13-15 centimeter) clay dish or divide among small broiler-safe bowls. Lightly dust with ground cinnamon and broil until toasted or bake for about 5-10 minutes in a 425˚F (220˚C) oven. This part is optional, but adds a nice contrast in texture.
Serve the Encharcada immediately or allow to cool first.