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1
In a food processor or blender, puree feta, oregano, tarrgon, thyme, garlic, and enough water to form a smooth liquid (about 1 cup). Place chicken into a large stockpot; add feta mixture. Fill stockpot with enough water to just cover chicken. Add bay leaf and stir. Cover and refrigerate 4-8 hours (ideally overnight).
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2
Heat barbecue to high, or preheat oven to 375u00b0F.
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3
Remove chicken from fridge about 20-30 minutes before cooking; transfer to a paper towel-lined surface. Discard brine. Using paper towel or a clean dish rag, dry chicken completely. Drizzle with olive oil and season with salt and pepper; rub into chicken and under skin.
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4
Open beer can; drink (or if it's 8 in the morning, pour our) half the beer. If barbecue/oven space is limited and you have to cook your chicken breast-side up, the can will need to be about a quarter full so it doesn't spill when horizontal. Insert beer can into chicken cavity.
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5
Carefully transfer bird upright onto barbecue or onto a roasting pan and into the oven (or laying down, if needed). Roast until chicken is cooked through and skin is crisp, abour 1 1/2 hours, depending on the size of your bird, or until an instant-read thermometer reaches 165u00b0F in the thickest part of the leg.
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6
Remove from heat. Allow to rest 15-20 minutes. Carve as desired and serve.