Begin by finely mincing 4 garlic cloves until they're nearly a paste.
Bring a pot of salted water to a boil and boil the pasta according to box instructions.
Drain pasta, set aside. Reserve at least ¼ cup of pasta water.
In a medium-large nonstick pan, add a drizzle of olive oil (about 1 tbsp) and 1 tablespoon of butter over medium heat.
Once the butter is melted, add the garlic and stir to saute.
Once the garlic is fragrant and almost golden, add the gochujang paste.
Use a wooden spoon or rubber spatula to mix the gochujang with the garlic, and let the gochujang paste cook for 1-3 minutes.
Once the gochujang is a slightly darker color, add the heavy cream and stir to combine.
Add the cooked pasta to the sauce in the pan and stir to combine.
Grate parmesan over the pasta and add salt as well as the other tablespoon of butter.
Stir until the butter is emulsified into the sauce.
If necessary, add pasta water to thin the sauce.
Serve hot and garnish with sliced scallions or chopped chives.