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5. Arrange chicken pieces on a work surface and season them with salt. Add chicken pieces to the broth, cover, and poach for 15 minutes, turning once halfway through. You want the chicken to poach gently and stay moist while picking up the flavor of the broth, so make sure the liquid does not get hotter than a gentle simmer. Turn off the heat and allow the chicken to cool in the liquid, covered, about 20 minutes.
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6. Remove the chicken pieces from the adobo broth (discard the broth) and transfer to a plate lined with paper towels. Pat dry.
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7. To fry the chicken: pour buttermilk into a large shallow bowl. In another bowl, combine flour, 1 teaspoon salt, paprika and pepper. Dip each chicken piece in buttermilk, shake off any excess liquid, dredge in flour mixture, turning to coat and transfer to a large plate. Let stand at room temp for 15 minutes. The flour coating will turn a little soft - that's a good thing.
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8. Meanwhile, fill a large deep cast-iron skillet about half-full with peanut oil. Heat the oil to 365 F. Cook chicken pieces 2 or 3 at a time for 8-10 minutes , turning every minute or so, depending on how thick the pieces of chicken are; wings will cook faster and drumsticks will take the longest. Be sure to keep the oil temperature at around 350 F to 365 F. The chicken is cooked when the internal temperature reaches at least 165 F. Using tongs, lift the chicken out of the oil and drain on paper towels. Season again with a little salt, and transfer to a platter.
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9. Serve the fried chicken with the waffle pieces and the dipping sauce. Eat it hot!