In a large stock pot or Dutch oven, heat the oil. Sauté the onion over medium-high heat until soft, 5 minutes. Add the parsnip and cook until beginning to turn golden brown, 3 more minutes. Stir in the garlic, ground cumin, ginger, cinnamon, salt, cayenne, and tomato paste. Cook until very fragrant, 2 minutes. Fold in the sweet potatoes, purple potatoes, and carrots. Cover with vegetable stock and bring to a boil. Reduce the heat to medium-low and simmer, uncovered, stirring occasionally, until the vegetables are tender, about 20 minutes.