Marinate the chicken: Combine vermouth, olive oil and crushed garlic. Pour and rub over the whole chicken, then season each side of the chicken with salt and let it sit in the marinade overnight or for a minimum of 8 hours. If you have time you can occasionally baste the chicken in the marinade every few hours.
Prepare to roast: Remove the chicken from the fridge. Scrape off all the crushed garlic pieces touching the chicken skin and discard (garlic burns very quickly in the oven and will leave dark and bitter pieces if roasted from the start).
Next, strain the left over vermouth oil from marinating and discard any extra garlic pieces. Keep oil aside. Heat oven to 200°C
Chop the potatoes into large chunks or wedges. Transfer to a roasting tin. Pour over vermouth oil, season with sea salt flakes and toss around the pan to combine.
Place the chicken into the middle of the roasting pan and gather potatoes around the chicken.
Roast for 50 minutes to 1 hour depending on the size of your bird. Halfway through roasting remove the pan from the oven, toss potatoes around the pan juices and fat and continue cooking.
When the chicken is ready, transfer the potatoes to a bowl, cover them with foil and keep warm. Let the chicken rest in the roasting tin for 20 minutes to release its juices.
Make the vermouth oregano sauce: After resting, transfer the chicken to a serving plate. Add 150ml vermouth to the roasting tray and scrape up all the chicken fat and juices. Transfer the liquid to a small pan along with the chicken stock and mustard. Bring to a boil then turn to simmer for a few minutes. Remove from heat, squeeze in some lemon juice, sprinkle with sea salt and the remaining oregano leaves.
Finishing the dish: Layer the warm potatoes around the chicken then spoon the vermouth oregano sauce evenly over the chicken and potatoes. Garnish with the remaining fresh oregano leaves and lemon wedges.