Step 1

Arrange a rack in center of oven; preheat to 475°. Toss squash with 2 Tbsp. oil in a 3-qt. baking dish; generously season with salt and pepper. Roast until softened, about 10 minutes.

Step 2

Toss sausage, onion, chile, and garlic with remaining 2 Tbsp. oil in a large bowl; season with salt and pepper. Scrape into dish with squash and toss to combine. Return to oven and roast until squash is tender and browned and other vegetables are softened, 10–15 minutes.

Step 3

Meanwhile, whisk eggs and milk in same bowl and stir in 1 cup cheese; season with salt and pepper.

Step 4

Reduce oven temperature to 350°. Carefully pour egg mixture into baking dish (rather than pouring it over the top, pick a spot near edge of dish and pour custard there; this will make for a prettier surface when baked). Top with remaining ¼ cup cheese. Bake until eggs are set but still slightly wobbly in the center and edges are puffed and brown, 10–15 minutes.

Step 5

Let egg bake cool 10 minutes. Serve topped with scallions and herbs.