4 chicken drumsticks
4 chicken thighs
1 2/3 cups, plus 1 1/2 tablespoons all-purpose flour
2 large eggs
1 teaspoon dried thyme
1 teaspoon sugar
1 tablespoon all-purpose flour, for the gravy
1 1/4 cups whole milk, for the gravy
Salt and freshly ground black pepper
1 teaspoon cajun seasoning vegetable oil, for deep frying
Combine 1 1/2 cups flour, the thyme, Cajun seasoning, and sugar in a large self-sealing plastic bag and season well with salt and pepper.
One at a time, add the drumsticks and thighs to the bag and shake until coated. Transfer to a wax paper-lined baking sheet.
Beat the eggs in a shallow dish. Dip the floured chicken in the egg, then return to the flour and coat again. Place the chicken on the baking sheet and chill for 30 minutes.
Fill a large deep saucepan halfway with oil and heat over high heat to 325°F (170°C). Add the chicken and deep-fry for about 20 minutes or until cooked through. Transfer to paper towels.
To make the cream gravy, transfer 2 tbsp of the frying oil to a saucepan. Whisk in the flour. Cook over low heat for 1 minute, then whisk in the milk. Cook, whisking often, until thickened. Season with salt and pepper.