Rub the chicken all over, including the cavity with 1 tablespoon salt, 1/4 teaspoon pepper and 1 teaspoon herbes de Provence. Refrigerate for at least 2 hours or up to overnight; bring the chicken to room temperature 30 minutes before grilling.
Put the potatoes in a large nonstick skillet and cover with water by 1/2 inch. Season with enough salt to taste like seawater. Bring to a boil and turn down to a simmer. Simmer potatoes until mostly cooked through, 3 to 4 minutes. Drain.
Prepare a grill for medium 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 and turn the remaining burners down to medium. 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. (Be sure to consult the grill manufacturer's guide for best results.)
Put the par-cooked potatoes in the bundt pan, along with the 3 smashed garlic cloves, 1 tablespoon olive oil, 1/2 teaspoon salt, and a few grinds of black pepper. Stir to combine.
Mix together the lemon zest with the remaining 1/4 cup olive oil, 1 teaspoon herbes de Provence and the clove grated garlic in a small bowl. Pat the chicken dry and spread a little of the oil mixture under the skin of the breasts and thighs. Brush or rub the rest all over the chicken. Sprinkle with a little more salt and pepper. Place the chicken cavity over the middle of the Bundt pan so that the chicken is sitting upright on top of the potatoes.
Carefully put the Bundt pan on the indirect side of the grill, with the back of the chicken facing the hotter side. Cover and cook for about 40 minutes. Carefully rotate the Bundt pan so that the breast is facing the hotter side of the grill, and give the potatoes a quick stir for even cooking. Cover and cook until an instant-read thermometer inserted in the thickest part of the thigh (avoiding the bone) reads at least 165 degrees F, 25 to 30 minutes more. Remove from the grill and let rest 20 minutes before carving.
Transfer the potatoes with a slotted spoon to a serving dish. Remove the pieces of garlic. Check for seasoning and add more salt and pepper, if necessary. Strain the fat and liquid in the bottom of the Bundt pan into a small saucepan, then spoon out most of the fat. Heat up the remaining liquid just enough to warm through. Squeeze in some lemon juice to taste and stir in the parsley. Serve the potatoes on the side and the cooking liquid drizzled over the carved chicken.
When using dried herbs, crush them in your hands before adding them to the other ingredients to bring out their flavor.
All grills are different and you know yours best. Cooking times may vary, so adjust as needed.
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