Step 1: Prepare all your ingredients. Slice the tofu, chop the kimchi, slice Spam and sausages, slice mushrooms and onion, and prepare the ramen noodles by discarding the seasoning packet. Set aside sliced green onions for garnish.
Step 2: In a large, shallow pot or wide pan, artfully arrange the sliced tofu, chopped kimchi, sliced Spam, sliced sausages, sliced mushrooms, and sliced onion. Place the instant ramen noodle block in an open section of the pot.
Step 3: In a small bowl, whisk together the gochujang, gochugaru, soy sauce, minced garlic, sugar, and black pepper to create the flavorful stew sauce.
Step 4: Pour the broth over the arranged ingredients in the pot. Then, spoon the prepared sauce mixture directly into the center of the pot.
Step 5: Place the pot over medium-high heat and bring the stew to a boil. Once boiling, reduce the heat to medium-low and let it simmer for about 10-15 minutes, or until the ingredients are cooked through and the broth is rich and flavorful. Gently stir the sauce into the broth after a few minutes of simmering.
Step 6: During the last 5 minutes of cooking, add the American cheese slices (if using) on top of the noodles or other ingredients, allowing them to melt into the stew. Stir in the sliced green onions just before serving.
Step 7: Serve the bubbling budae jjigae directly from the pot at the table, encouraging everyone to enjoy it communally with plenty of steamed white rice.