Cut the calabaza into uniform pieces, roughly 1 ½ inches in size, ensuring even cooking. Place the pieces into a large pot and pour in the water. Stir in the salt and bring the mixture to a rolling boil over high heat. Once boiling, lower the heat to medium-low, cover, and allow the calabaza to simmer until tender, about 30 minutes.
Using a colander, drain the cooked calabaza thoroughly, allowing it to rest for at least 15 minutes to eliminate excess moisture. This step ensures a better texture for the fritters.
Transfer the softened calabaza to a mixing bowl. Sprinkle in the sugar and sift in the flour, then add the vanilla extract. Using a spoon or fork, mix until a thick, cohesive batter forms.
In a large frying pan, heat the vegetable oil to 350°F. Test the oil by dropping a small portion of batter—if it sizzles immediately, the oil is ready for frying.
Scoop tablespoon-sized portions of the batter and gently drop them into the hot oil, ensuring not to overcrowd the pan. Fry until each fritter develops a golden, crispy exterior, about 2 minutes per side.
Once fried to perfection, transfer the fritters onto a plate lined with paper towels to drain any excess oil. Serve warm and enjoy their delicate sweetness and soft interior.