Wash the baby potatoes thoroughly. If some are larger than others, halve or quarter them so they are all roughly the same size for even cooking. There's no need to peel them.
Place the potatoes in a large pot of salted water. Bring to a boil and parboil for 8-10 minutes, just until a fork can pierce them with a little resistance. They should not be fully cooked. Drain thoroughly and let them steam dry for a few minutes.
While the potatoes are cooling, prepare the marinade. In a large mixing bowl, whisk together the yogurt, mustard oil, lemon juice, tandoori masala, kashmiri chili powder, garlic powder, ginger powder, cumin, coriander, amchur powder, turmeric, and salt until a smooth paste forms.
Add the parboiled and dried potatoes to the bowl with the marinade. Using a spatula or your hands, gently toss until every potato piece is evenly and generously coated in the spicy yogurt mixture.
Cover the bowl and allow the potatoes to marinate for at least 15 minutes at room temperature. For deeper flavor, you can marinate them in the refrigerator for up to 4 hours.
Preheat your air fryer to 400°F (200°C) for 3 minutes. Lightly grease the air fryer basket with oil.
Arrange the marinated potatoes in the basket in a single layer, ensuring they are not crowded. You may need to cook in batches. Reserve any extra marinade left in the bowl.
Air fry at 400°F (200°C) for 18-22 minutes, shaking the basket or turning the potatoes halfway through the cooking time. They are done when the edges are crispy and charred in spots, and the potatoes are cooked through.
Garnish with freshly chopped cilantro and serve immediately with lemon wedges on the side for squeezing over the top. Perfect as a side with grilled meats or with a cooling raita.