In a medium bowl, sift together flour and salt. In a separate container mix egg and water. Place flour/salt and egg/water mixtures in the refrigerator and keep cold until ready to deep fry. It is important to keep batter and batter ingredients cold at all times so that the tempura stays crispy.
Begin heating the oil in your deep fryer of choice to 350 degrees.
Dust the vegetables with cornstarch to absorb any excess water so that the batter will stick better.
Just before you are ready to deep fry, remove batter ingredients from the refrigerator. Add egg/water to flour mixture. Stir just to combine, some lumps will remain. Do not over mix and keep cold at all times. If possible, put bowl over an ice bath while you work. For crispy tempura, the goal is the prevent the activation of the wheat gluten. So work quickly and keep everything cold.
Coat the vegetables in batter and add to the deep fryer. Pay attention to the oil temperature and keep it steady at all times. As you add vegetables, the temperature will drop slightly, so only add a few at a time to allow the temperature to recover. Additionally, do not crowd the fryer. Cook in the order and for the time indicated below and then remove to a wire rack or a plate lined with a paper towel to drain the excess oil. Between batches, remove any crumbs from the oil so that they do not burn and affect the taste of the oil.
Serve with unagi sauce for dipping.
If you are frying large batches, some of the first vegetables may loose their crispness over time. If this happens, place them on a baking rack over a baking sheet and broil for a few minutes until batter recrisps.
To reheat leftovers, either put under the broiler as described above, or put in an Air Fryer and reheat at 375 degrees for 3 to 4 minutes until recrisped and heated through. Flip vegetables half way through cooking time.