Prepare dashi broth. Combine all ingredients in a medium stockpot. Bring to a boil over high heat. Reduce to a simmer and cook for 20 minutes. Remove from heat and strain stock, discarding ingredients.
Heat 1 tablespoon oil in a wide pot over medium-high heat. Add onion, carrot, and garlic and saute until onions have softened, about 3-4 minutes. Arrange spam, pork belly, kimchi, tofu, and rice cakes in the pot. Pour in dashi broth and bring to a boil.
Mix together seasoning spice including chili powder, chili paste, soy sauce, and rice wine. Add to soup and mix together. Reduce heat to a simmer and cook for another 5 minutes.
Add ramen noodles and cook until tender, about 2-3 minutes. Remove from heat and serve.