Arrange bread, uncovered, on a baking sheet; let dry 8 hours or overnight, stirring once or twice.
Heat oven to 375 degrees F. Butter a 9x13-inch baking dish; set aside. Melt butter in a large skillet over medium-high heat. Add onions, celery, sage, thyme and pepper and cook 10 to 12 minutes, stirring occasionally, until vegetables start to brown around the edges. Add broth and bring to a simmer; cook 3 minutes to reduce slightly.
Fold together vegetable-broth mixture, bread, eggs and parsley in a large heat-proof bowl until evenly moistened. Loosely spoon into baking dish and bake, uncovered, about 30 minutes or until the top is golden brown.