How to Make It
Heat oven to 375° F. Oil a 2 ½- to 3-quart baking dish.
Heat the oil in a large skillet over medium-high heat. Add the onions and cook, stirring frequently, until beginning to soften, 4 to 5 minutes. Add the squash, season with ½ teaspoon salt and ¼ teaspoon pepper, and cook, tossing frequently, until just tender, 8 to 10 minutes more. Stir in the sage. Let cool for 10 minutes.
In a large bowl, whisk together the eggs, milk, and ¼ teaspoon each salt and pepper. Add the bread, cheese, and squash mixture and toss to coat.
Transfer to the prepared baking dish and bake until golden brown and set, 55 to 60 minutes.