Prepare the onion mixture up to 3 days ahead. Cover and store in the refrigerator. You can also toast the bread up to 3 days ahead; store it in an airtight container. Before serving, combine the onion mixture and bread, then add the broth and bake.
Preheat oven to 350°.
Arrange the bread cubes in single layers on 2 baking sheets. Bake at 350° for 18 minutes or until toasted. Remove from oven.
Increase oven temperature to 375°.
Melt butter in a large nonstick skillet over medium-high heat. Add onion and celery; sauté 4 minutes or until tender. Add ham and next 5 ingredients (ham through salt); sauté 2 minutes.
Combine onion mixture and bread, tossing gently to combine. Add broth; toss gently to coat. Spoon mixture into a 13 x 9-inch baking dish coated with cooking spray.
Cover and bake at 375° for 10 minutes. Uncover and bake an additional 35 minutes or until golden brown.
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