Line a baking sheet with parchment, then spray parchment with oil.
In a large bowl, combine the cream cheese, vegetables, sesame oil, and soy sauce until well combined.
To wrap the wontons, prepare a space with the wrappers, the filling, and a small bowl of water. Place a heaping tablespoon of filling in the center of 1 wrapper. With your finger or a pastry brush, brush water along all four edges of the wrapper. Fold two adjacent sides together, pressing the seams to adhere. Join the next adjacent corner to the point, adhering the seams, then close the final corner of the wonton, pressing firmly.
Place wontons on prepared baking sheet. Repeat with all wonton wrappers.
Whisk egg into a small bowl with a splash of water, then brush egg wash lightly onto wontons. Spray with cooking oil, then add to the oven.
Bake the wontons for 10-12 minutes, or until golden brown all over. Tops of wontons will darken first.
Remove from the oven and let cool slightly before serving.