Bring a large pot of water to a boil and add noodles. Boil the noodles for 8 minutes until soft (just beyond al dente). Reserve 1 1/2 cups of the noodle cooking water, drain the noodles, and rinse with cold water to cool to room temperature. Drain well and reserve.
While the noodles are boiling, heat 2 tablespoons of vegetable oil on high heat in a wok or large skillet until lightly smoking. Add diced pork belly and shoulder and render for 2 minutes.
Add ginger and garlic and sauté for 1 minute, being mindful not to burn. Add carrots, potatoes, onions, and zucchini and sauté for 6 minutes, until vegetables are softened.
Mix in the chunjang, sugar, 1 cup of noodle water, and salt to taste. Cook for 7 minutes, or until the sauce has thickened and the potatoes are fully cooked. If you need to add more noodle water, do so.
Divide noodles into 2 bowls and top with warm sauce. Garnish with julienned zucchini and pickled yellow daikon, if using. As an alternative, the sauce can be served over cooked rice for a dish called "jjajangbap."