For the glaze: In a pot on medium-high heat, add the root beer, ketchup, sugar, lime juice, garlic and ginger. Whisk together until the mixture begins to boil and the ketchup and sugar are dissolved into the root beer. Lower to a simmer and when it begins to reduce in volume and thicken, turn off the heat and add the pepper. Allow to steep in the residual heat for 10 minutes, then discard the pepper and stir the glaze.
For the wings: In a large paper bag, add the flour, cornstarch, a nice pinch of salt and a few grinds of black pepper. Crimp it shut and gently toss it to mix the contents. In batches, add a few wings and toss them from side to side to fully coat. Remove to a wire rack and allow to rest until the flour soaks into the skin, about 15 minutes. Repeat the process for 2 dry coats. After the second resting period, the wings are ready to fry.
In a deep fryer or deep heavy pot, add enough oil to fill to about 4 inches. Heat the oil until a deep-fry thermometer registers 350 degrees F. Add the wings in batches to keep the temperature and fry each batch 12 minutes. Remove the wings to a paper towel-lined plate and sprinkle immediately with a pinch of salt.
In batches, add a bit of the glaze to a large bowl and a few wings, then toss them to coat. Remove the wings to a platter, top with a spritz of lime and a sprinkle of sesame seeds and serve.