Bring a large pot of salted water to a boil and cook the pasta until al dente. Reserve one by four cup pasta water, then drain the pasta.
Heat olive oil or butter in a large pan over medium heat. Add the chopped onion and cook until soft and translucent, then stir in the garlic and cook briefly until fragrant.
Lower the heat and add the gochujang. Stir well and cook for about one minute, then add soy sauce and brown sugar or honey and mix until combined.
Pour in the heavy cream and stir continuously until the sauce becomes smooth and creamy.
Add the cooked pasta to the sauce and toss until evenly coated, adding reserved pasta water a little at a time if needed to loosen the sauce.
Season with black pepper and chili flakes if using. Remove from heat, garnish with Parmesan cheese and green onions, and serve warm.
