Cut the vegetables into ~1 cm sticks.
In a large bowl, combine the sifted flour with cornstarch and baking soda.
Add ice in a large bowl and place another bowl inside. Add the aquafaba in the smaller bowl and whisk it until frothy. Pour in the cold sparkling water, then mix in the dry ingredients: psyllium husks, flour, cornstarch and baking soda.
Whisk until it reaches the consistency of a crepe batter (similar to the consistency of cooking cream). Be careful not to whisk it too much or it will get too thick.
Pour the oil into a pot and place it on the stove, on medium heat. Wait until it reaches 180C (360F).
Dust each piece of vegetable with some flour, then gently add it to the batter and mix it in. You can use a pair of chopsticks for this.
Test to see if the oil is ready by dropping a small tempura piece in it. If it goes to the bottom and then comes up immediately, it's the right temperature. Otherwise, if the veggies don't drop to the bottom, it's too hot.
Fry ~3 pieces at a time and don't overcrowd the pan or they will end up greasy and even stick together.
Cook is vegetable tempura for 1-2 minutes on one side, then gently turn it on the other side for one more minute, until both sides are golden.
Fish the veggies out using a slotted spoon and place them on a paper towel.
Serve right away with the dipping sauce.