Place all the dipping sauce ingredients in a microwave-safe bowl. Whisk and warm in the microwave for 1-2 minutes, just long enough for the sugar to dissolve. Whisk again and set aside.
In a large bowl, beat together the flour, water, egg and salt. Mix in the thawed hash browns, then set the batter aside to rest.
Preheat two non-stick skillets to medium high heat. Slice all the veggies julienne (long thin strips) and mix into the batter. Pepper to taste. If the batter still seems very thick after the veggies are mixed in, add 2-3 tablespoons of water and mix well.
Now add a little oil to each skillet and swirl around. Ladle enough veggie batter into each skillet to completely cover the bottom. Fry for 4-5 minutes, per side. Repeat with remaining batter. Cut the Korean pancakes into wedges and serve warm with the dipping sauce.
Using a 12-inch skillets, you should have enough batter to make 4 large pancakes.