In a large pot, heat vegetable shortening until a deep-fry thermometer reaches 375 degrees F. Line a sheet tray with a wire rack.
Using kitchen shears or a sharp knife, separate the chicken wings into the drummettes and wings, discarding the wing tip joint.
In a large bowl, whisk together eggs, cream, cayenne, 1 tablespoon salt and black pepper. In a paper bag, shake together flour, cornstarch and 1 tablespoon salt. Place chicken in egg mixture and toss well to coat. Place chicken in batches in the bag of flour mixture. Shake well to coat. Set on wire rack to let coating set, 20 minutes.
Meanwhile make the Honey BBQ Sauce and the Spicy Butter Sauce. In a small saucepan, bring the ingredients for the Honey BBQ Sauce to a simmer over medium-high heat. Reduce heat and cook until sauce has reduced by half, about 12 minutes, stirring frequently. In another saucepan, bring the ingredients for the Spicy Butter Sauce to a simmer. Remove from heat and let basil infuse in butter for at least 15 minutes. Remove basil.
When oil is at the right temperature, add chicken, working in batches, and fry until cooked through and crispy, about 13 minutes. Season chicken with salt then immediately toss, taking turns with batches, in the Honey BBQ sauce, or the Spicy Butter Sauce or sprinkle with the lemon and lime zest.