Season pork slivers with ¾ teaspoon of salt and the pepper and set aside.
Set a large pot over medium-high heat and add the sesame oil.
Once oil starts to shimmer, add the slivers of pork tenderloin. Cook until the pork is browned, 1½ to 2 minutes. Use tongs to turn the pork over and brown the other side, about 1 minute more. Transfer to a plate and set aside.
To the pot, add the sliced scallion whites and cook, stirring often, until soft, for 1 to 1½ minutes. Stir in the garlic, and once fragrant, after about 30 seconds, stir in the gochujang, gochugaru and tofu.
Add the kimchi, water, rice vinegar, soy sauce and remaining 1½ teaspoons of salt, bring to a simmer and reduce the heat to medium-low.
Simmer 20 minutes, return the pork to the pot and simmer for 1 minute more. Serve the soup in bowls sprinkled with the sliced green scallions with a heaping addition of steamed white rice.
Kimchi, gochujang and gochugaru are available in many supermarkets' international sections or at a local Korean or Asian grocer.