Step 1: In a medium bowl, combine the softened cream cheese, powdered sugar, and vanilla extract. Beat with an electric mixer or whisk until the mixture is completely smooth and creamy.
Step 2: If using fresh strawberries, finely dice them and gently fold them into the cream cheese mixture. If using strawberry jam, simply stir it in until well combined.
Step 3: Lay a wonton wrapper flat on a clean surface, positioning it like a diamond. Place about 1 tablespoon of the strawberry cheesecake filling in the center. Lightly moisten the edges of the wrapper with water. Fold one corner over the filling to meet the opposite corner, forming a triangle, and press firmly along the edges to seal completely.
Step 4: In a deep skillet or pot, heat the vegetable oil over medium-high heat until it reaches 350°F (175°C). Use a kitchen thermometer to ensure accuracy.
Step 5: Carefully lower the assembled wontons into the hot oil, frying in small batches to avoid overcrowding. Fry for 2-3 minutes, turning occasionally, until they are golden brown and crispy on all sides. Remove and place on a paper towel-lined plate to drain.
Step 6: Once slightly cooled but still warm, dust the fried wontons generously with powdered sugar. Serve immediately and enjoy!