Heat 1 Tbsp. vegetable oil in a large skillet over medium-high. Add cabbage and cook, tossing often, until edges are browned, about 4 minutes. Reduce heat to low and continue to cook, tossing often, until thickest parts of cabbage leaves are tender, about 4 minutes longer. Remove from heat and set skillet aside.

Place udon in a large heatproof bowl (or pot if you don’t have one) and cover with 6 cups boiling water. Let sit 1 minute, stirring to break up noodles, then drain in a colander. Transfer noodles back to bowl and toss with sesame oil. Transfer cabbage to bowl with noodles. Wipe out skillet.

Heat remaining 1 Tbsp. vegetable oil in same skillet over medium-high and add pork, breaking up and spreading across surface of pan with a spatula or tongs. Cook pork, undisturbed, until underside is brown, about 3 minutes. When pork is browned, break up meat into small bits. Cook, tossing, just until there’s no more pink, about 1 minute.

Add chopped scallions (the pale parts), ginger, and red pepper. Continue to cook, tossing often, until scallions are softened and bottom of skillet has started to brown, about 1 minute.

Add udon mixture, mirin, and soy sauce and cook, tossing constantly, until noodles are coated in sauce, about 45 seconds. Remove from heat and fold in 1 Tbsp. sesame seeds and dark-green parts of scallions. Top with more sesame seeds before serving.