Preheat the oven to 375°F (190°C). Grease a large baking dish or Dutch oven.
Pat the chicken very dry with paper towels. Season generously inside and out with salt and pepper.
Prepare the garlic-thyme butter: heat olive oil in a small skillet, add the minced shallot and garlic, and cook for 2 minutes. Remove from heat and stir in butter, thyme, parsley, and lemon zest.
Gently loosen the chicken skin using your fingers or the back of a spoon. Spread the butter under and over the skin.
Stuff the cavity with lemon pieces, shallots, and garlic. Tie the legs together if desired.
Toss the potatoes with olive oil, salt, pepper, ( add more thyme and parsley, if you'd like to) and shallots (can use less or substitute with onions).
Place the chicken in the center of the baking dish and arrange the potatoes around it. Pour chicken stock over the potatoes.
Roast for 1 hour, then carefully turn the chicken and roast for 15 more minutes, until golden. You can roast covered for the first 30 minutes, then uncovered for the remaining time.
Broil for 3-4 minutes for extra crisp skin, watching closely to prevent burning.
The chicken is done when a thermometer inserted into the thickest part of the breast reads 165°F (74°C).
Let the chicken rest for 10 minutes before carving. Serve warm.