Preheat the oven to 350 degrees F. Butter a medium baking dish.
Slice the yellow squash and zucchini lengthwise into quarters, then cut into 1/2-inch-thick wedges. Place the yellow squash, zucchini and carrots in a saucepan, barely cover with water and salt well. Bring to a boil; reduce the heat to medium and cover. Cook about 20 minutes, until the vegetables are very soft.
Meanwhile, warm 3 tablespoons of the butter in a medium skillet over medium-low heat. Stir in the onion and cook slowly until very soft and translucent, 6 to 8 minutes. Add the garlic and cook an additional minute. Scrape the mixture into a mixing bowl. Wipe out the skillet, return it to medium-low heat, and add to it the remaining tablespoon of butter. Stir in 1/2 cup of the cracker crumbs and cook briefly until the crumbs are golden. Scrape them onto a small plate and reserve them.
Drain the squash mixture, mashing the vegetables just a bit. Spoon it into the mixing bowl. Stir in the remaining 3/4 cup of cracker crumbs, cheese and a good splash or two of the pepper sauce. Salt and pepper generously to taste. Stir in the eggs and spoon the mixture into the prepared baking dish. Scatter the toasted cracker crumbs over the top. Bake uncovered for about 30 minutes, until golden brown and lightly firm in the center. Serve hot.
Recipe courtesy of Cheryl Alters-Jamison & Bill Jamison, American Home Cooking, Broadway Books