In a large pot over medium heat, warm the oil. Add the tomato paste and cook for about 2-3 minutes, stirring often, or until the tomato paste starts to caramelize/stick to the pot.
Stir in the curry powder, chili flakes (if using), and black pepper for about 30 more seconds to bloom the spices in the oil.
Stir in the water, potatoes, soy sauce, fish sauce, and ½ teaspoon salt. Bring to a boil over high heat, then simmer rapidly over medium heat for about 7-10 minutes or until the potatoes are almost cooked through.
Meanwhile, season the salmon flesh with the remaining ½ teaspoon salt.
Add the salmon, skin side facing up, and nestle it into the liquid so it’s submerged. Gently simmer for about 6-12 minutes or until the salmon is cooked through (this depends greatly on the thickness of the fish - remove a filet and try to flake the thickest part with two forks to see if it’s cooked through. It will continue to cook from the residual heat of the soup, so it’s best to under cook it slightly).
Transfer the salmon to a cutting board, skin-side-up, to cool off. Stir in the greens and turn off the heat (or continue to simmer for a minute or two if they are very fibrous greens that need more cooking).
Meanwhile, transfer about ½-1 cup of the broth to a bowl or liquid measuring cup. Add the peanut butter and whisk until smooth and combined. Pour back into the pot along with the lime juice.
Remove the skin from the salmon (it should peel off easily), then flake it up into big chunks and stir it back into the pot.
Serve topped with cilantro, peanuts, and a squeeze of lime.