In large saucepan filled halfway with water, add potatoes, sweet potatoes, parsnips and turnip. Bring water to boil and then lower heat to medium and cook, partially covered, until vegetables are very tender, 15 to 20 minutes. Drain vegetables. Transfer them to medium bowl and coarsely mash. Cover mashed vegetables to keep warm.
While vegetables cook, in small skillet, heat canola oil over medium-high heat. Add coriander and chiles and stir-fry until coriander seeds are reddish brown and chiles are blackened, about 1 minute. Turn off heat. Using slotted spoon, transfer chiles and coriander to mortar. Reserve spiced oil. Grind chilies and coriander with pestle, scraping spice blend into centre with spatula until it has consistency of finely ground black pepper.
Once vegetables are smashed, add reserved spiced oil into vegetables along with ground spice blend, cilantro and salt. Stir well to combine and serve warm.