Place a large pot or Dutch oven over medium high heat. Add the olive oil and diced onion to the pot and stir to mix. Cook the onions for 4-5 minutes, stirring occasionally.
Meanwhile, as the onions are sautéeing, add the chopped carrots to the food processor and pulse until riced (don't start with whole carrot sticks; chop them first and then add to the food processor). Transfer the riced carrots to the pot with the sautéeing onions. Add the garlic and dried basil. Stir well to combine.
Finally, add the chopped kale to the food processor and pulse 3-4 times, or until chopped into small pieces (you can also do this by hand, but I find it easier to do it with the food processor).
Transfer the kale and cauliflower to the pot and stir well to combine. Cook everything together for 3-4 minutes before adding a pinch of salt and the vegetable broth. Bring to a boil. Once boiling, reduce heat to low and cover. Simmer for 20 minutes, or until all veggies are cooked.
With the vegetables fully cooked, stir in the coconut milk and season with salt and pepper to taste.
Serve with fresh bread, crackers and Tabasco sauce for a little heat, if desired.