In a large heavy-bottom pot bring water, salt and sugar to a rolling boil. Remove from heat and allow the water to cool to room temperature. Immerse chicken in the cooled water, pour in beer, cover and refrigerate for 8, up to overnight. Remove chicken from brine at least 3 hours prior to cooking, rinse under cold water and pat entirely dry with paper towel. Discard brine. Place chicken uncovered back in the refrigerator for 1 hour to further dry and tighten the skin.
Remove chicken from refrigerator 2 hours prior to grilling and rest on the counter to begin returning the bird to room temperature. Meanwhile, drizzle the chicken with olive oil inside and out, then massage a liberal amount of dry rub, salt and peppercorn into all portions of the chicken. Open a room temperature beer, drink (or discard) half the contents, then slide the whole chicken onto the beer can.
Preheat the grill to low-medium heat and simply place the beer can-stuffed chicken over the coolest, indirectly-heated grill grates – balancing the bird upright upon the beer can and it’s 2 legs. Slowly roast the chicken for 60-90 minutes, intermittently rotating and basting the bird every 30 minutes with browned butter, until internal temperature in the dark thigh meat reaches 165F and juices run clear.
Carefully remove the chicken from the grill (attentive to the scolding metal beer can positioned inside the chicken) and transfer to a cutting board. Tent with tin foil and rest for 15-20 minutes before discarding the beer. Carve in serving portions, season additionally to taste, garnish with lemon zest and fresh herbs, then plate alongside seasonal vegetables and an ice cold craft brew.