Divide the cubed bread between 2 baking sheets and bake until crispy and golden brown, about 8 minutes.
Heat the olive oil in a large skillet over medium-high heat. Cook the sausage, stirring and breaking up the meat, until browned, 8 to 10 minutes; remove to a plate using a slotted spoon. Lower the heat to medium and add the leeks, carrots, celery, garlic and sage. Cook, stirring occasionally, until the vegetables are tender, 8 to 10 minutes. Season with salt and pepper.
Combine the toasted bread, sausage and vegetables in a large bowl. In a medium bowl, whisk together the stock and apple cider, then add it to the bread mixture. Mix to combine.
Grease two 9-inch square baking pans with the butter. Divide the stuffing between the baking pans and brush with the egg wash. Bake until the top is crispy and the stuffing is hot through the center, 35 to 45 minutes.