Thinly slice the onion. Cut the eggplant into long bite-sized pieces. Slice the kabocha about ¼ inch (5 mm) thick, and slice the zucchini into ½ inch (1 cm) rounds. Score a shallow "X" on the bottom of the tomato.
Season the chicken drumettes with salt, black pepper, and garlic powder. Heat a large pot over medium heat and cook until both sides are golden brown.
Add the onion and tomato. Cook until the onion has softened and the tomato is soft on both sides. Crush the tomato with a spoon, then remove and discard the loosened skin.
Pour in the water, cover, and simmer for about 15 minutes.
While the chicken is simmering, heat the cooking oil in a separate pan and lightly fry the eggplant, kabocha, and zucchini until just tender.
Break the Japanese curry roux cubes into the pot and stir until completely dissolved. Simmer for another 2 to 3 minutes until the curry thickens. If you'd like to make it your own, stir in a small amount of your favorite secret ingredient, such as strawberry jam, barbecue sauce, chocolate, coffee, or tonkatsu sauce.
Serve Japanese curry rice by spooning cooked rice onto each plate, ladling the curry over the rice, and topping with the fried summer vegetables.