Bring a large pot of water to a boil and cook pasta according to package to al dente. Drain pasta and save about 1.25 cups of reserved pasta water.

In a pan over medium-high heat, add butter and garlic and stir for 30 secs until fragrant. Then add gochujang and mix well for another 30 seconds. Then add coconut milk and parmesan cheese and stir until dissolved, about 1 min. Then add pasta water and mix until smooth. Let the sauce simmer a few minutes until thickened and creamy. Add additional pasta water as needed to ensure the sauce is creamy.

Add cooked pasta to sauce and stir well to combine. Transfer pasta to a plate and top with optional burrata cheese and chili oil.