The whole idea here is to scrub and trim the vegetables and cut them in fairly large pieces of a more or less uniform size so that they will roast evenly.
Trim the eggplants, quarter them lengthwise, then slice about ½ inch thick. Toss the pieces in a bowl with a couple teaspoons of salt and transfer to a colander to drain while you prepare the remaining vegetables.
Cut the Kabocha squash in half, scoop out and discard the seeds, and cut each half into 1-inch wedges. Trim off the skin with a very sharp knife, leaving only the firm, dark-yellow flesh, and cut it in 1-inch squares.
Peel the onions, halve them lengthwise, then cut each half into 6 or 8 chunks. Trim the bell peppers and cut them in pieces about 1 inch square.
Scrub the potatoes, trim away any rough spots, and cut them in ¾-inch dice. Peel the garlic cloves.
Put all the vegetables except the eggplant into your largest bowl, add the olive oil, rosemary, oregano, 1½ teaspoons of salt, and as much fresh pepper as you think you might like. Mix everything together thoroughly. All the vegetables should be lightly coated with oil and herbs. Now rinse and drain the eggplant pieces, and mix them into the other vegetables.
Spread the vegetables out on 2 medium-sized baking sheets, and roast them in a 400° oven for about 1½ hours. After the first 30 minutes, turn them with a spatula, stir them around a bit, and reverse their positions in the oven so the one that was underneath can have a turn on top. Move them around again after 30 minutes, and after that check them every 15 minutes.
They’re done when the biggest chunk of squash is tender, when golden brown patches appear here and there, when the peppers look soft and the potatoes have crisp edges—when they just look done.
Variation: Substitute 7–8 medium zucchini or crookneck squashes for the eggplant.