Peel all potatoes, parsnips, turnips, and celery root. Cut into 1-inch cubes. Place vegetables in the large pot, and add salt and water, just enough to cover them. Bring water to boil.
Reduce heat and cook, covered until the vegetables are tender (approximately 15-20 minutes).
When vegetables are done, discharge the water and transfer into a large bowl.
Next, prepare the corn mixture. In a large pan, heat oil over medium-high heat. Add onions and cook for 5 minutes, covered. Stir once. Uncover and add corn, minced garlic, mayo, and black pepper. Reduce the heat, and cook for 2 more minutes. Add this vegetable mixture into a small bowl and set aside.
Then pour the coconut milk over the root vegetables.
Next, mash them with a potato masher a few minutes. Use a strong wooden spoon to beat further with coconut milk until it is well combined.
Add corn mixture and fresh thyme. Gently mix and serve immediately! Enjoy!