If the wings have not been pre-cut, straighten the wings and cut at each joint. You can save the wing tips for chicken stock.
Heat the vegetable oil to 350°F in a large heavy-duty pot or deep fryer and fry the wings for 8 to 10 minutes. The chicken will be done when the internal temperature reaches 165°F and the juices from the chicken run clear. Remove the wings from the oil and let them drain on a wire rack over a baking sheet.
To make the Buffalo sauce, melt the butter in a saucepan over medium heat. When the butter has melted, add the hot sauce. Cook until the mixture starts to bubble, whisking constantly. Remove the sauce from the heat and add the remaining ingredients (except for the ranch or blue cheese dressing), whisking constantly for 2 minutes to prevent the egg yolk from scrambling.
Place the fried wings into a large bowl. Pour the sauce over the wings and toss until all the wings are coated. Serve with ranch or blue cheese dressing.