Add penne pasta to boiling water and cook according to package instructions; cook to al dente. Drain, rinse and set aside.

Using a large wok or skillet, heat the sesame oil over medium-high heat. Add the onions, mushrooms and chopped beef and cook until the beef is no longer pink, for about 4-5 minutes. Add the chopped kimchi and mix together. After a minute or so, add the gochujang and cooked penne pasta and mix to combine, making sure the penne gets nicely coated. Let cook for a few minutes. Remove from heat. Garnish with diced green onions and serve immediately.