Peel and mash the ripe bananas in a large bowl. Set aside.
In a large saucepan, combine the granulated sugar, water, and cinnamon stick.
Cook over medium heat, stirring occasionally, until the sugar has dissolved and the mixture comes to a simmer.
Add the mashed bananas to the saucepan, stirring well to combine.
Reduce the heat to low and let the mixture simmer, stirring frequently, for about 30-40 minutes, or until the mixture thickens and turns a deep golden color. Be careful not to let it burn.
Stir in the vanilla extract, lemon juice, ground nutmeg, and ground cinnamon (if using). Mix well.
Remove the cinnamon stick and let the mixture cool to room temperature.
Transfer the Doce de Banana to sterilized jars and store in the refrigerator.
Enjoy your meal!