In a bowl, combine ingredients for the dipping sauce and divide among 4 small ramekins.
In a large pot over medium-high heat, heat 3 inches of oil. Arrange shrimp and/or vegetables near the stove for quick dipping and frying.
Whisk the dry ingredients for the batter together then whisk in the club soda to combine. Stir in the sesame seeds. Using a slotted spoon or spider, dip shrimp and/or vegetables a few pieces at a time, into the batter then add to the hot oil and fry until golden. Remove to baking rack set over a baking sheet to drain. Allow oil to reheat before frying the next batch.
Serve tempura with dipping sauce alongside.