Simmer water and kombu in a large pot for 10 minutes to create a flavorful dashi broth.
Add chicken drumsticks, carrot, and kabocha squash to the broth. Cook for 15-20 minutes until chicken is tender and vegetables are fork-tender.
Stir in curry powder, Japanese dark soy sauce, sake, mirin, chicken bouillon powder, and chili bean sauce. Mix well to combine all seasonings.
Add shrimp, shimeji mushrooms, Napa cabbage, Japanese leek, and bell pepper to the pot. Cook for 5-8 minutes until vegetables are soft and shrimp turn pink and are fully cooked.
Add the cross-scored tomato and shredded cheese to the pot. Allow cheese to melt and tomato to warm through.
Serve immediately with cooked ramen noodles on the side for dipping and eating alongside the curry nabe.