To make the dipping sauce, combine all ingredients into a small bowl. Mix well, and set aside.
Combine all of your chopped/sliced vegetables into a large mixing bowl. You want everything to be fairly uniformly chopped so they cook evenly, and slice the carrots as evenly and thin as possible so that they cook faster.
Sprinkle 1/3 cup of flour (I used GF flour), tapioca starch, and salt over the vegetables and mix well with chopsticks until everything is nicely dusted/coated with the flour blend. If you find things aren't totally coated, add another tablespoon or two of the flour. It depends on how big your vegetables are, so it's always easier to add flour than take it out.
Add 1/4 cup of sparkling water over the mixture, and toss until the flour is just hydrated. If it's still looking pretty dry, add another couple tablespoons (I use between 1/4 - 1/3 cup, depending on the day).
Preheat a skillet over medium heat. Add about a tablespoon of oil to the pan and swirl around to coat. You can either cook as one large pancake, or do what I prefer, which is a couple smaller pancakes on the pan. Mound some of the "batter" (it won't be very liquidly unless you like it that way), and flatten slightly with the back of a spatula. Cook until one side is browned, then flip and press to cook the other side. It should be about 2-3 minutes per side, depending on how thick you've made the pancakes.
Remove from the pan once both sides are nice and crisp and your vegetables look cooked through.
Arrange on a plate, garnish with some extra green onion and/or cilantro if you like, then enjoy! Tear the pancake up and dip in that sauce.