Preheat the oven to 350 degrees.
Make the caramel: Put the sugar and water in a small saucepan and set to medium heat. As the sugar melts, a light amber color will begin to appear. Leave the caramel to form without stirring. Swirl the pan around a bit and wait until the caramel is medium to rich amber color, takes about 10-12 minutes. Be sure to keep an eye on it because it will burn very quickly,
Pour the amber caramel into your flanera or large ramekin. Swirl the flanera carefully to make sure the entire bottom of the pan is well coated with the caramel. Set aside to cool so that the caramel sets.
In a large bowl pot place your peeled and cubed pumpkin and 1 cinnamon stick. Fill with enough water to cover the pumpkin. Boil until the calabaza is fork tender. Drain the water and remove the cinnamon stick. Place the cooked pumpkin in a food processor and pulse until finely pureed. Reserve 2 cups of pumpkin and set aside.
Make the custard: Pour the milk, condensed milk, sugar, salt, vanilla extract, sugar and 2 cinnamon sticks into a medium saucepan over medium low heat. Whisk as the condensed milk melts to ensure it is completely mixed into the milk.
Make a cornstarch slurry with the cornstarch and about 2-3 tablespoons of the milk mixture. Add the cornstarch slurry to the custard mix and stir to combine.
Once everything is well combined, remove from the heat and mix in the 2 cups of pureed pumpkin. Once well incorporated, remove the cinnamon sticks.
In a medium mixing bowl, mix together the egg yolks and eggs. Mix vigorously until foamy and a light yellow color.
Temper the warm milk mixture into the whisked eggs by adding a couple tablespoons at a time while whisking to ensure you don't end up with scrambled eggs. Once half the milk mixture has been added to the eggs you can pour the rest in slowly while whisking.
Place your flanera or large flan ramekin inside a 9x13 pan.
Prepare to pour your flan into the flanera. While pouring it into the ramekin, have the custard mix go through a mesh strainer to ensure any egg or large pumpkin bits don't make their way into your flan.
Place the top on your flanera and pour in warm-hot water around the ramekin so that it comes to about half of the way up.
Bake for 1 hour and 10 minutes or until set. Remove from the oven carefully and allow to cool slightly on the counter. When cool, transfer to the refrigerator and chill for at least 3 hours.
Once ready to serve, run a knife along the edge of the flan and then invert the flan onto your serving dish.