Heat oven to 375° F. Butter a 3-quart baking dish. Place the bread on a large rimmed baking sheet and toast, tossing once, until golden, 12 to 15 minutes. Transfer to a large bowl.
Cook the sausage in a large skillet over medium heat, breaking it up, until browned, 7 minutes. Add to the bread.
Wipe out the skillet and melt the butter over medium heat. Add the leeks, carrots, and ½ teaspoon each salt and pepper and cook, stirring occasionally, until soft, 10 to 12 minutes. Add the broth and raisins; bring to a boil. Add to the bread.
Add the parsley and eggs to the bread mixture and toss to combine. Transfer to the prepared baking dish. Cover loosely with buttered foil and bake for 30 minutes. Uncover and bake until golden, 15 to 20 minutes.