Bring a large pot of salted water to a boil, and cook spaghetti until tender with a bite, about 12 minutes. Scoop out 1/2 cup pasta water; set aside. Drain spaghetti.

Cook and stir ground beef in a large skillet until browned, about 6 to 7 minutes.

Add tomato paste and gochujang to the meat, bring to a simmer, and cook for 3 to 4 minutes. Add heavy cream and stir until fully incorporated. Season with salt and pepper.