Heat the oil over medium heat in a heavy, oven-safe pot. Add the potato cubes and fry until golden brown. Transfer the fried potatoes to a strainer, sprinkle with a little salt, and mix to coat evenly. Pour out the used oil.
In the same pot, heat fresh oil to about 0.2” (0.5 cm) deep. Add the drumsticks, season with salt and ground black pepper, and fry until deeply golden on all sides. Remove the chicken from the pot and set aside.
In the same pot, fry the onions until caramelized. Towards the end, add the garlic and fry for another 2-3 minutes.
Return the chicken and fried potatoes to the pot. Add orange juice, water, honey, salt, ground black pepper, and thyme leaves. Bring to a boil, then reduce the heat to low. Cover the pot and cook for about an hour.
Preheat the oven to 390°F (200°C). After an hour, transfer the pot to the oven with the lid on for about 30 minutes.
Remove the lid and continue baking for another 20-25 minutes.
Remove from the oven and serve hot.