Cut a few shallow slits into each chicken drumstick, and place into a resealable plastic bag; set aside. Heat 5 tablespoons of vegetable oil in a Dutch oven or large pot over medium-high heat. Stir in the onion, garlic, and ginger. Cook and stir until the onion has turned golden brown, about 7 minutes. Remove the pot from the heat, and use a slotted spoon to scoop the onion mixture into a blender. Leave as much oil in the pot as you can, and set aside. Add 3 tablespoons white vinegar, coriander, cumin, garam masala, black pepper, salt, turmeric, and cayenne pepper. Puree until smooth, then pour into the bag with the chicken; mix until the chicken is evenly coated, and squeeze out excess air. Marinate at room temperature for 1 hour, or in the refrigerator for 3 hours or longer.
After the chicken has marinated, heat the oil left in the Dutch oven over high heat, and stir in the curry leaves and mustard seeds. Once the mustard seeds have finished popping and have turned gray, remove the chicken from its marinade, and cook until browned on all sides, about 5 minutes. Pour in the remaining marinade and water. Bring to a simmer, then reduce heat to medium-low, cover, and simmer 20 minutes.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
While the chicken is cooking, deep fry the potato cubes until golden brown. Drain on a paper towel-lined plate. Once the chicken has cooked for 20 minutes, stir in the potatoes and 2 tablespoons of white vinegar. Recover, and continue to simmer until the chicken is no longer pink at the bone, at least more 10 minutes.
We have determined the nutritional value of oil for deep frying based on a retention value of 10% after cooking. The exact amount will vary depending on cooking time and temperature, ingredient density, and the specific type of oil used.