In a large pot over medium heat, add the oil, onion, carrots, celery, and ½ teaspoon salt. Cook for 5 minutes, stirring occasionally, or until softened.
Stir in the garlic, paprika, cumin, thyme, and tomato paste. Cook, stirring often, for 1 minute.
Stir in the potatoes, cauliflower, water, rice (if using), mustard, soy sauce, and remaining 1 teaspoon salt. Increase the heat to high to bring to a boil. Give it a stir, then reduce the heat to medium to keep it at a rapid simmer for 20 minutes, stirring halfway through, or until potatoes and rice are cooked through.
Transfer about 3 cups of the soup (try to get lots of potato/cauliflower/rice and enough liquid to blend easily - this will help thicken up the soup) to a high-speed blender and blend until smooth (making sure to let the steam escape). Stir it back into the soup.
Stir in the kale and place salmon chunks on top of the soup. Bring to a gentle simmer, then cover with a lid and simmer for 3-5 minutes, or until the salmon is cooked through.
Keep the salmon in chunks or flake them up into the soup. Serve topped with black pepper, fresh herbs (if using) and saltine crackers (if using).