Step 1

Take the chicken and wine out of the fridge and allow to come room temperature, 15 to 30 minutes.

Step 2

Prepare a grill for medium-high indirect heat: For gas grills (with 3 or more burners), turn all the burners to medium-high heat; after about 15 minutes turn off one of the middle burners (2 if you have a grill with 4 or more burners). For charcoal grills, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. The grill should be around 400 degrees F so adjust the burners or air-flow vents as necessary to maintain that temperature. (Be sure to consult the grill manufacturer’s guide for the best results.)

Step 3

Combine the olive oil, oregano, rosemary leaves, thyme leaves, garlic and 2 teaspoons salt in a food processor and purée into a paste.

Step 4

Open the wine and pour off 1/3 cup for another use. Tuck the rosemary and thyme sprigs into the can. Rub the chicken all over, including the cavity, with the garlic-herb paste. Place the wine can on a baking sheet. Place the cavity of the chicken onto the wine can so the can is holding up the chicken and its legs act as a stabilizer. Carefully transfer the chicken and can onto the indirect side of the grill. Close the lid and grill until the chicken is cooked through and an instant-read thermometer inserted into the thickest part of the thigh reads 165 degrees F, 1 hour to 1 hour 15 minutes.

Step 5

Carefully remove the chicken and can from the grill and gently pull the chicken off the can. Tent the chicken with aluminum foil. Pour the remaining wine (about 1 cup) into a small saucepan. Add the peppercorns and set on the direct heat side of the grill. Bring to a boil and reduce by half, 15 to 20 minutes. Remove from the heat and whisk in the cheese until smooth.

Step 6

Serve the chicken with the sauce.