In a large pan or bowl, combine warm water with kosher salt until salt is dissolved. Add ice cubes to cool down the water. Whisk in black pepper, sliced garlic cloves and squeeze lemon and add the rind into the brine. 

Lower chicken into brine, cover and refrigerate at least one hour and up to 4 hours.

Drain chicken and discard brine. Pat dry with a paper towel and place on a rimmed baking sheet. 

Using poultry shears, cut down the breast bone and the back bone, cutting the chicken in half. The backbone can be removed if desired. We left it intact because we debone the chicken and use the carcasses to make homemade chicken broth. 

Prepare a grill fire to about 325° using hickory or pecan for smoke flavor.

Spray chicken halves with olive oil on both sides. 

Combine the dry rub ingredients together in a bowl: brown sugar, garlic, chili powder, thyme, kosher salt, black pepper and smoked paprika. 

Sprinkle over chicken on both sides. 

Grill chicken over indirect fire with the grill closed, about 45 minutes. Check with a digital thermometer cooking until internal temperature reaches 165° near the thick part of the thigh.

Remove from grill and allow chicken to rest about 10 minutes before slicing and serving.