Make the brine: Combine the beer, brown sugar, salt, orange zest, orange juice and cardamom pods in a bowl; stir until the sugar and salt dissolve.
Put the chicken in a gallon-size resealable plastic bag and add the brine; seal and refrigerate 2 hours.
Prepare the grill: For a charcoal grill, pile 3 to 4 pounds briquettes in the grill; ignite and let burn until the coals are ashy. For a gas grill, preheat to high.
Prepare the chicken: Remove from the brine and pat dry; reserve the orange zest and cardamom. Rub the olive oil all over the skin. Loosen the skin on the breasts and legs with your fingers; rub 1 garlic clove under and over the skin. Combine the brown sugar, coriander, cumin, paprika, allspice, 1 1/2 teaspoons salt and a few grinds of pepper; rub under and over the skin of the chicken and inside the cavity.
Pour half of the remaining beer can into a disposable 8-inch-square pan. Add the reserved orange zest to the pan. Poke 3 or 4 holes into the top sides of the beer can using a paring knife. Add the remaining 3 smashed garlic cloves and the reserved cardamom pods to the can.
For a charcoal grill, bank the coals to both sides in two piles; nestle the pan with the beer between the coals and replace the top grill grate. For a gas grill, reduce the heat to medium on one side and turn off the burners on the other; place the pan under the grate on the unlit side.
Set the chicken over the beer can, inserting the can into the cavity so 1 inch of the can is exposed. Set on the grill grates over the drip pan so the chicken balances on the can and legs like a tripod. Cover the grill and cook until the chicken is golden brown and a thermometer inserted into the thickest part of the thigh registers 165 degrees F. If using charcoal, this will take about 1 hour 20 minutes; add a handful of briquettes to each bank of coals every 30 minutes to maintain the heat. If using gas, it will take about 1 hour 5 minutes; carefully rotate the chicken halfway through.
Remove the chicken from the grill, discard the can and transfer to a cutting board; let rest 10 minutes before carving.
Photograph by Con Poulos
Courtesy of Food Network Magazine