In a large pot, bring water to a boil and cook the potatoes for 15 minutes, or until they are soft enough to mash. Drain and mash the potatoes with a potato masher or fork.
In a frying pan, melt the vegan butter over medium heat. Add the chopped onion and sauté until it becomes soft and translucent. Add the chopped carrot and celery, and cook for 3-4 minutes until they are soft. Add the frozen green peas and corn kernels and cook for another 2-3 minutes. Season with salt, black pepper, garlic powder, onion powder, and paprika.
Add the mashed potatoes to the frying pan and mix everything well. Remove from heat and let it cool.
In a small bowl, mix the all-purpose flour and plant-based milk to make a batter.
Shape the potato mixture into small balls or patties. Dip each ball or patty into the batter and then coat with breadcrumbs.
Heat vegetable oil in a frying pan. Fry the korokke in the oil over medium heat until they are golden brown on both sides. Use a kitchen thermometer to ensure the oil is at 350°F.
Once done, place the korokke on a paper towel-lined plate to remove excess oil.
Serve hot with your favorite dipping sauce.