Combine 1 tablespoon oregano, 1 ½ teaspoons salt, pepper, and zest of 1 lemon in a small bowl. Rub chicken with spice mixture all over and refrigerate for 1 hour or overnight.
When ready to cook, remove chicken from the refrigerator 30 minutes in advance to bring to room temperature.
Preheat the oven to 400 degrees F (200 degrees C).
Arrange potatoes, fennel, and shallots in the bottom of a large roasting dish.
Scatter whole peeled garlic cloves amongst vegetables. Season with remaining 1 teaspoon salt, pepper, and ½ tablespoon dried oregano. Add 2 lemon halves to the roasting dish.
Pour chicken broth into the dish (vegetables just just be submerged). Set chicken on top and coat with olive oil. Cover with foil.
Roast in the preheated oven for 40 minutes. Remove foil for browning and continue roasting until chicken is no longer pink at the bone and the juices run clear, 20 to 45 minutes. An instant-read thermometer inserted near the bone should read at least 165 degrees F (74 degrees C). If you have a larger chicken that needs to cook longer, cover again towards the end of the cook time to prevent too much browning.
Remove chicken from the oven, cover to keep warm, and allow to rest for 15 minutes. Squeeze lemon halves over cooked chicken and potatoes and serve.
