In a large bowl, season the pork with 1/2 tsp. of the salt. In a small bowl, mix the hoisin sauce, soy sauce, and vinegar.
Heat 2 Tbs. of the oil in a 12-inch nonstick skillet or large stir-fry pan over medium-high heat until shimmering hot. Add the pork and cook, stirring, until it browns and loses most of its raw appearance, about 2 minutes. Transfer to a plate.
Add the remaining 1 Tbs. oil to the skillet. Add the garlic, and once it begins to sizzle, add the cabbage and pepper. Sprinkle with the remaining 1/2 tsp. salt and cook, stirring, until the cabbage starts to wilt, about 2 minutes.
Add the hoisin mixture, the pork, and half of the chives and cook, tossing, until heated through, about 1 minute. Let sit for 2 minutes off the heat (the cabbage will exude some liquid and form a rich broth), toss well again, and serve sprinkled with the remaining chives.