Dry the bread cubes completely before starting. If they are not already stale, spread them over baking sheets and dry them in a low oven until crisp but not browned.

Melt the butter in a skillet over medium heat. Add the onion and celery, then cook for 5 to 7 minutes, stirring occasionally, until the vegetables soften; stir in the parsley.

Place the dry bread cubes in a large mixing bowl. Sprinkle in the poultry seasoning, sage, salt, and black pepper, tossing gently to distribute the seasonings.

Pour the warm butter, onion, celery, and parsley mixture over the seasoned bread. Toss carefully so the butter coats the cubes without crushing them.

Whisk the chicken broth and lightly beaten eggs together in a separate bowl. Pour the liquid over the bread mixture a little at a time, tossing until evenly moistened; the mixture should be moist but not wet or soupy.

Grease a 5- to 6-quart slow cooker and transfer the stuffing inside. Arrange it loosely rather than packing it down so heat can circulate and the center cooks evenly.

Cover and cook on LOW for about 4 hours, or on HIGH for approximately 2 to 3 hours, until hot throughout and lightly set. For food safety, check that the center reaches 165°F, and remove the lid for the final 20 to 30 minutes if the stuffing seems too moist.