Step 1: In a medium bowl, beat the softened cream cheese, granulated sugar, vanilla extract, and a pinch of salt with an electric mixer until smooth and creamy. Ensure there are no lumps.
Step 2: Lay an egg roll wrapper on a clean, dry surface with one corner pointing towards you (diamond shape). Place about 1-2 tablespoons of the cheesecake filling just below the center.
Step 3: Fold the bottom corner over the filling and tuck it in tightly. Fold in the left and right corners towards the center. Then, roll the wrapper upwards tightly, brushing the top corner with a little water to seal it completely. Repeat with the remaining wrappers and filling.
Step 4: Heat about 2-3 inches of vegetable oil in a large, heavy-bottomed pot or deep fryer to 350°F (175°C). Use a candy thermometer to monitor the temperature.
Step 5: Carefully place a few egg rolls into the hot oil, ensuring not to overcrowd the pot. Fry for 2-4 minutes, turning occasionally, until they are golden brown and crispy on all sides.
Step 6: Using tongs or a slotted spoon, remove the fried egg rolls and place them on a plate lined with paper towels to drain excess oil.
Step 7: Gently warm the caramel sauce in a small saucepan over low heat or in the microwave until it reaches your desired consistency. You may add a pinch of sea salt if desired.
Step 8: Dust the warm golden cheesecake egg rolls with powdered sugar, if desired, and serve immediately with the warm caramel dip on the side.