Heat the vegetable oil in a deep, heavy pot to 325°F.
Carefully add the chickpeas in batches and fry for 4 minutes, until pale gold and mostly set.
Remove with a slotted spoon and spread on a paper towel-lined tray. Let rest and cool for 10 minutes.
Raise the oil temperature to 375°F.
Return the chickpeas to the oil in batches and fry for 3 to 4 minutes more, until deeply golden and audibly crackling when stirred.
Drain on fresh paper towels and season immediately with salt.
While the chickpeas fry, combine the brown sugar, bourbon extract, apple cider vinegar, soy sauce, cayenne, and smoked paprika in a small saucepan.
Bring to a simmer over medium heat and cook for 3 to 4 minutes, until slightly thickened.
Remove from heat and stir in the butter until glossy.
Toss the hot, double-fried chickpeas with the warm bourbon sauce just before serving.