Heat oil in a fryer or a heavy pan to 350 degrees F.
Prepare your veggies by cutting and trimming as required. Try to ensure consistent-sized pieces to help even cooking. Pat veggies to dry.
Stir together the dry ingredients in a large bowl. Stir in the cold water with chopsticks until combined, leaving a few lumps. It should be the consistency of a thick cream. Add more water, if required.
Dip the veggies in the batter and allow batter to drip off a little.
Cook dipped veggies a few at a time until batter has crisped and browned a little. Different veggies will take different amounts of cooking. Root veggies will probably take 4-5 minutes, while onions may only take a minute or two. Some experimenting will be needed. It is important not to overcrowd the veggies while they are cooking and that the oil is kept at the proper temperature.
Once veggies are cooked, let rest on a paper towel for just a moment and then serve hot with dipping sauce. These are best when eaten right away! Enjoy!
Dipping Sauce
Whisk together the ingredients in a small bowl. Make this ahead of time so that you are ready to dip and eat as soon as the tempura veggies are done.