Heat the olive oil in a large skillet over medium-high heat. Cook the potatoes in the hot oil until browned on all sides, about 10 minutes. Remove from skillet and reserve.
Reduce the heat to medium, and cook the onions in the skillet until translucent, 2 to 4 minutes. Stir the garlic, ginger, turmeric, cumin seeds, and salt and pepper into the onions. Cook until fragrant, about 1 minute. Return the potatoes to the skillet and cook until almost done, about 15 minutes.
Pour the coconut milk over the potatoes; stir in the tomato puree and chopped parsley. Cook until potatoes are cooked through and sauce has thickened, about 5 additional minutes.