In a large bowl, mix the cream cheese, vanilla extract, and ⅔ cup sugar until smooth and well-combined. In a small bowl, beat the egg with ⅓ cup water.

Place wonton wrappers on a work surface and cover with a moist kitchen towel. Working one wonton at a time, lay out a wonton wrapper and place 1 heaping teaspoon of the cream cheese mixture in center. Moisten the edges of the wrappers with a fingertip dipped in the egg wash mixture.

Fold one corner of the wrapper over to create a triangle. Moisten the two side corners of the triangle with egg wash and cross them over the center of the wonton. Transfer to a large plate. Repeat until all of the wontons have been sealed, and cover with a lightly dampened kitchen towel. Set aside.

Toss the remaining ⅓ cup sugar and cinnamon in a paper bag. Set aside.

In a microwave safe bowl, combine the dulce de leche, Nutella, and heavy cream. Cover with a paper plate and microwave on high for 30 seconds. Stir well. Continue to microwave and stir in 15 second intervals until pourable and smooth. Keep warm.

Heat oil in a Dutch oven, wok, or deep fryer to 350°F (175°C). Add wontons to the oil in batches of 4 and fry, turning and agitating constantly until just beginning to turn golden, about 30 seconds (see note). Place the fried wontons on a paper towel-lined plate to absorb excess oil. Transfer to the bag with the cinnamon sugar and toss to coat. Transfer wontons to a wire rack set in a rimmed baking sheet. Repeat until all of the wontons are cooked.

Serve immediately with Nutella dipping sauce.