Italian Sausage and Bread Stuffing

(3/4- to 1-pound) round Italian loaf, cut into 1-inch cubes (8 cups)

olive oil, divided

sweet Italian sausage, casings removed, divided

unsalted butter, cut into pieces

medium onions, chopped

large celery ribs, chopped

garlic cloves, minced

large eggs, lightly beaten

heavy cream, divided

turkey giblet stock or reduced-sodium chicken broth

grated Parmigiano-Reggiano (2 ounces)

coarsely chopped flat-leaf parsley

-qt shallow ceramic or glass baking dish (14x10x2 3/4 inches)