Cook the noodles al dente in salted water, according to package directions. Drain, reserving 1 cup of the noodle-cooking water.

In a large skillet over medium-high heat, cook the bacon or pork belly, turning occasionally, until browned and crisp, about 5 minutes. Drain off any excess oil in the pan.

Heat a small saucepan over medium-high heat. Add the gochujang paste and garlic and cook, stirring, for about 1 minute. Add the cream and bring almost to a boil. Reduce the heat and simmer until the sauce thickens, 2 to 3 minutes.

Stir in the soy sauce and add a splash of the reserved noodle cooking water to loosen the sauce a bit.

Meanwhile, drain any excess bacon fat from the skillet you used to cook it. Heat the skillet over medium-high heat and fry 4 eggs, either over easy or sunny side up, until done to your liking. Transfer the cooked eggs to a plate.

Add the drained pasta and the sauce to the skillet and cook over medium heat, tossing the noodles with tongs, Cook for about 2 more minutes, adding additional reserved pasta cooking water, a little at a time as needed, to ensure the sauce coats the noodles well. Add the bacon and toss to combine.

Divide the noodles among 4 serving bowls, top each with a fried egg, and garnish with the green onions. Top with Parmesan cheese, if desired and serve immediately.