Bring a medium pot of salted water to a boil over high heat. Add lo mein noodles and cook until just al dente, stirring occasionally, about 5 minutes. Drain and toss noodles with sesame oil to prevent clumping.
Meanwhile, place a large skillet over high heat. Add butter, gochujang, and shallots. Cook, stirring, until shallots are softened and gochujang is caramelized. Add cabbage and carrots. Cook 3 minutes. Add asparagus and cook for an additional 2 minutes, until all vegetables are crisp tender. Add water, scraping bottom of pan to deglaze. Add noodles to skillet, fold to combine, and season to taste with additional salt. Divide among serving bowls and serve immediately, each portion topped with an egg yolk, scallions, and chile flakes, if desired.