Chop the eggplant, peppers, and zucchini into large 1″ chunks, about 1 inch, keeping the eggplant separate from the rest of the veggies.
Heat 3 Tbsp of the oil in a large skillet over medium heat. Add the eggplant pieces and stir. They will absorb the oil fairly quickly, but it shouldn’t stick. Stir fry the eggplant for about 10 minutes, stirring frequently, until softened.
Heat the remaining 1 Tbsp of oil in a large pot over medium heat. Add the minced onion and garlic and stir for a few minutes, until fragrant.
Add the remaining veggies, including the eggplant and the can of tomatoes. Add the bay leaf also.
Cover with a lid and simmer over medium heat for 15-20 minutes, stirring often to prevent it from sticking.
Remove from heat and stir in the tablespoon of miso paste. Miso paste is delicate and shouldn't be added during cooking.
Remove the bay leaf.
Divide into 4 servings and accompany with your choice of protein and onigiri rice balls or atop a bed of cooked rice.