Marinate the chicken: In a large bowl, combine the bourbon, soy sauce, and lemon juice. Trim and discard any visible fat on the chicken thighs. Cut each thigh lengthwise into 5 to 6 strips. Toss the strips in the bourbon mixture. Cover and refrigerate for 24 hours.
Make the dip: Blend half the cheese with the mayonnaise in a food processor until smooth. Add the sour cream and cider vinegar and process until the mixture has the consistency of creamy mayonnaise. Add the scallions, parsley, and dill and process again briefly. Add the remaining cheese, process very briefly (the dip should be slightly chunky), and remove from the food processor. Season to taste with salt, pepper, and cayenne. Wrap well and refrigerate for up to four days.
Make the sauce: In a small saucepan, whisk together the hot sauce, melted butter, salt, and cornstarch mixture. Heat while whisking constantly until the mixture comes to a boil. The sauce should be smooth and slightly thickened. Remove from the heat and keep warm.
Finish the dish: Heat the oven to 250ºF. Pour enough oil into a wok or deep, heavy pot to reach about 2 inches. Heat the oil to 365ºF or until the oil shimmers and the air 2 inches above the oil feels hot.
Drain the chicken well and pat dry with paper towels. Season the chicken with the 1/2 tsp. pepper. Spread the flour in a wide, shallow container and dredge one-third of the thigh strips, shaking off any excess flour. Carefully put the strips one at a time in the hot oil. Fry until the strips are golden brown, about 7 minutes. Remove from the oil and drain on paper towels. Repeat this process until all the chicken has been fried.
Put the fried chicken in a large bowl. Toss with the warm sauce and spread in a single layer on a baking sheet. Heat in the oven for about 5 minutes so the sauce is absorbed. Serve immediately with the dip, peppers, cucumber, and celery.