In a large heavy-bottomed saucepan, pour in enough vegetable oil to fill the pan about 1/3 of the way. Heat over medium heat until a deep-frying thermometer, inserted in the oil, reaches 375 degrees F. (If you dont have a thermometer a cube of bread will brown in about 2 minutes.)
While the oil is heating, in a medium bowl, whisk together the flour, baking powder and baking soda. Add the club soda and sesame oil. Stir until just combined and still lumpy.
Dip the vegetables in the batter and fry, 3 or 4 at a time, until the batter is golden and crispy, about 60 to 70 seconds. Drain on paper towels.
Arrange the vegetables on a platter and serve the soy sauce alongside as a dipping sauce.