Pour enough oil into a frying pan to cover the bottom 1/3-inch deep; add garlic, cumin, salt, turmeric, and black pepper. Heat oil mixture over medium heat.
Cook and stir potatoes in the hot oil, turning occasionally, until cooked through, golden brown, and crisp on the outside, 10 to 15 minutes. Add fresh cilantro and curry paste and stir to coat. Fry until cilantro is dark green and crisp, about 1 more minute. Remove potatoes with a slotted spoon and transfer to serving dish.