Drizzle a 2-quart baking dish, such as an 8-inch square, with 2 teaspoons of the olive oil.

Cut 8 ounces crusty French bread or baguette into 1-inch cubes. Place in the baking dish and arrange into an even layer.

Thinly slice 2 medium scallions, keeping the dark green parts separate from the white and light green parts.

Grate 4 ounces sharp cheddar cheese on the large holes of a box grater (about 1 cup).

Remove 8 ounces uncooked breakfast sausage from the casings if needed.

Heat the remaining 2 teaspoons of olive oil in a large skillet over medium-high heat until shimmering.

Add the sausage and white and light green scallion parts. Cook, breaking up the sausage into bite-sized pieces with a wooden spoon, until the sausage is browned and cooked through, about 5 minutes.

Transfer the sausage mixture evenly over the bread. Sprinkle with the cheese.

Place 6 large eggs, 1 cup whole milk or 2% milk, 1 teaspoon smoked paprika, ½ teaspoon kosher salt, and ¼ teaspoon black pepper in a large bowl and whisk until combined.

Pour evenly over the bread mixture. Press down on the bread so it soaks up the liquid.

Cover and refrigerate for at least 8 or up to 24 hours.

Arrange a rack in the middle of the oven and heat the oven to 350ºF.

If the casserole has been refrigerated, let it sit at room temperature while the oven is heating.

Uncover and bake until lightly browned on top and a tester inserted into the center comes out clean, 30 to 50 minutes.

Let cool for 5 minutes before serving. Sprinkle with more paprika and garnish with the reserved dark green scallion parts.