Set a rack over a baking sheet; if a rack is not available, a paper towel-lined baking tray will work as well.
In a medium bowl, whisk together melted butter and egg until smooth.
Add onion, chives, both sugars, baking powder and salt; mix until no lumps are present.
Mix in cornmeal and flour; while whisking, stream in buttermilk and incorporate until mixture is smooth but not runny; it should be thick enough to easily scoop and drop into hot oil.
In a medium skillet with high sides or a deep cast-iron skillet, over medium-high heat, heat 2-inches oil to 350°F.
Working in batches, scoop 1-tablespoon balls of the batter and carefully drop nto the oil.
Fry until one side is golden brown; about 1 minute.
Using a spatula or spoon, flip and fry for another 1 minute until golden brown on all sides.
Using a slotted spoon, remove hush puppies from hot oil and place on the prepared rack to drain.
Sprinkle with a little more salt.
Notes
Once the hush puppies have cooled completely, store in a resealable plastic bag or container fitted with a lid that's lined with a paper towel to absorb any excess oil. Hush puppies can be stored in the refrigerator for 3 - 5 days.