In a medium bowl, toss the pork, 1/2 Tbs. of the soy sauce, and 1/8 tsp. pepper.
Heat 1 Tbs. of the oil in a 12-inch nonstick skillet over medium-high heat until you see the first wisp of smoke. Swirl to coat the pan, then add half of the pork and stir-fry until brown in spots and no longer pink, about 2 minutes. Transfer to a bowl. Add another 1 Tbs. of the oil to the skillet and repeat with the remaining pork.
Add the remaining 1 Tbs. of the oil to the pan and swirl to coat. Add the mushrooms and scallions and cook, stirring, until the mushrooms are shrunken in size and the scallions are wilted, 2 to 3 minutes. Stir in the garlic and cook until fragrant, about 30 seconds.
Add the kimchi, mirin, and the remaining 1/2 Tbs. soy sauce and cook, stirring frequently, until the liquid released by the kimchi is reduced to about 1/3 cup, about 3 minutes. (The amount of liquid released by the kimchi is somewhat unpredictable— if there is an excessive amount, cook until it reduces or spoon some of it off.) Add the pork and any accumulated juices and cook until heated through, 1 to 2 minutes more. Drizzle with the sesame oil and stir well. Season to taste with salt and pepper, sprinkle with the sesame seeds, and serve.