Tomato-Cheddar Strata

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Unsalted butter, at room temperature, for the baking dish

3 cups half-and-half

1/4 cup grated Parmesan

10 large eggs

Kosher salt and freshly ground black pepper

One 12-ounce loaf sourdough bread, preferably stale, crust removed, cut into 1-inch cubes (about 6 cups)

2 cups shredded sharp Cheddar

1 cup sun-dried tomatoes packed in oil, drained, patted dry and chopped

1/4 cup thinly sliced scallions