Special equipment: a deep-frying thermometer
For the herb mayo: Combine the lemon juice, mayonnaise, basil, chives, a pinch of salt and a few grinds of pepper in a blender or food processor. Puree until smooth with small flecks of green. Transfer to a bowl and refrigerate until ready to serve.
For the hush puppies: Line a plate with a paper towel. Fill a wide, large pot with about 1 1/2 inches of oil and bring to 360 degrees F over medium-high heat. Meanwhile, whisk the cornmeal, flour, baking powder, baking soda, cayenne, granulated garlic and salt together in a large bowl. In another bowl, whisk together the egg, onion, and buttermilk. Pour the buttermilk mixture into the flour mixture and stir until just combined. Working in batches, use 2 spoons to carefully drop rounded tablespoonfuls of batter into the oil. Fry until golden brown all over, about 3 minutes; remove the hushpuppies with a slotted spoon and place on the paper towel-lined plate to drain briefly. Serve immediately with the herb mayo on the side for dipping.