How to Make It
In a small saucepan, combine 1 cup of the milk with 3/4 cup of kosher salt and the sugar and stir over moderate heat just until the sugar and salt dissolve, about 2 minutes. Transfer to a large, deep bowl and add the remaining 3 cups of milk. Add the chicken pieces and refrigerate for 4 hours. Drain the chicken and pat thoroughly dry.
In a bowl, mix the buttermilk, eggs, 2 tablespoons of salt, the paprika, hot sauce and pepper. Whisk in the baking powder and baking soda. Put half of the flour in a large bowl. Working with a few pieces at a time, dredge the chicken in the flour, tapping off any excess. Dip the chicken in the buttermilk, letting the excess drip off; return the chicken to the flour and turn to coat. Transfer to a rack. Repeat with the remaining chicken, adding more flour as needed. If the flour becomes too lumpy, sift it.
Heat the oil in 2 large, deep skillets until shimmering. Working in batches, add the chicken to the skillets in a single layer, without crowding, and fry over moderate heat, turning occasionally, until deep golden and cooked through, 18 to 20 minutes; an instant-read thermometer inserted near the bone should register 160°. Drain the chicken on wire racks lined with paper towels and fry the remaining pieces. Serve hot or warm.