Gather all ingredients.
Combine ricotta, powdered sugar, cream cheese, vanilla, and salt in a food processor and process until smooth and combined. Transfer to a large bowl and fold in chocolate chips or pistachios. Transfer to the freezer, uncovered, to cool for about 20 minutes or until firm.
Pour oil to a depth of 1 ½ inches in a large Dutch oven or heavy-bottomed pot; heat oil over medium-high to 360 degrees F (180 degrees C).
Prepare a small bowl of water. On a clean work surface, spoon about 2 heaping teaspoons of cream cheese mixture into the center of a wonton wrapper, and using a clean finger, wet all sides of the wonton. Fold opposite corners on the diagonal and bring in the other two sides to make a pouch or envelope. Press gently to seal all edges, ensuring there are no gaps.
Working in batches, adjusting heat as needed, fry rangoons until golden brown, about 2 minutes, gently stirring as needed to cook all sides.
Transfer to a wire rack. Serve warm, drizzled with chocolate syrup. Dust with powdered sugar.
