Fill a large pot with salted water and bring it to a rolling boil. Add the pasta and cook 1 minute less than package instructions. Reserve 1/2 cup pasta water before draining.

After draining, return pasta to the pot and drizzle with olive oil, tossing to coat. Set aside.

In the same pot, melt butter over medium heat, then add minced garlic and sauté for 30 seconds to 1 minute until fragrant.

Stir in gochujang and toast for 1-2 minutes until darkened and fragrant.

Pour in heavy cream and half of the reserved pasta water, stirring continuously until smooth. Season with salt, black pepper, and smoked paprika.

Add cooked pasta and 1/4 cup Parmesan cheese to the sauce. Stir until cheese melts and sauce coats noodles. Cook for about a minute to thicken.

Taste and adjust seasoning. Garnish with additional Parmesan cheese and parsley if desired.