In a medium pot, heat the oil and then saute the onion for a few minutes, till softening. Add the garlic, celery, carrot, salt and spices. Saute for about 5 minutes, mixing frequently, until the vegetables are soft and letting off wonderful aromas.
Add the cauliflower and potato to the pot. Add enough water to cover the vegetables.
Bring to a boil and reduce to a simmer. Cook for about 45 minutes and then puree with an immersion blender.
Ladle the soup into bowls and garnish with cheddar.