Add pine nuts into a skillet and heat over medium heat. Stir the pine nuts frequently. When the pine nuts start to turn golden brown, turn to medium low heat. Cook and stir until for another minute, until the pine nuts turn light brown. Transfer to a plate to cool.
Add oil to the same skillet and turn to medium high heat. Add green onion and stir a few times. Add carrot and corn. Stir and cook until the corn is thawed and the carrot starts to turn tender. If the skillet gets too hot, turn to medium or medium low heat. Add cucumber. Season with salt and sugar. Stir and cook for another minute, until the cucumber is cooked.
Turn off heat. Whisk the potato starch slurry again and swirl it into the skillet. Stir to mix well. (*see footnote 2)
Taste the dish and add a bit more salt if necessary.
Add toasted pine nuts. Stir to mix well.
If you are using frozen peas instead of the cucumber, add the peas when you're adding frozen corns. They takes longer to cook than cucumber.
I added the chicken stock slurry at the end, so that the dish would be like the one that you’d find in a Chinese restaurant. If you want to make the dish vegetarian, simple replace the chicken stock with water. You can skip this step, too. The finished dish will be slightly dry, but still taste good.