Preheat oven to 350 degrees. Line a baking sheet with aluminum foil and spread the cubed bread in one layer. Toast in the oven for 5 minutes to dry it out. Set aside.
In a skillet over medium heat, melt the margarine. Add the celery and sauté for a few minutes to soften. Add the onion and sauté until tender. Set aside.
In a large mixing bowl, toss the bread with the thyme, salt, pepper and eggs. Add in the sauteed veggies. Add the broth and gently fold in. If you happen to be making this at the same time as my Slow Cooker Mashed Potatoes, you can use the leftover reserved broth here.
Transfer bread mix into a greased 9 x 13 baking dish and bake uncovered for 20 minutes.