Preheat oven to 250° F. Place the bread cubes on two rimmed baking sheets. Place bread in the oven for 15 minutes, stirring and rotating the pans halfway through the cook time, until bread cubes are dried out but not browned. Remove from oven and set aside. (Alternatively, you can let the bread cubes sit in a loosely covered bowl on the counter for 24 hours to dry them out.)
Increase oven temperature to 350° F. Lightly grease a 13x9-inch baking dish.
Place the butter in a large Dutch oven or large skillet over medium high heat. Once the butter is melted, add the onion and celery to the pan. Saute, stirring occasionally, until the vegetables have softened, about 6 minutes.
Add the garlic, parsley, sage, rosemary, thyme, salt and pepper to the pan and cook, stirring, for 1 minute. Remove pan from heat.
In a liquid measuring cup or medium bowl, whisk together the broth and the egg.
If the bread cubes will fit in the pot with the onion, celery and herbs, add them to the pot and stir to combine. If not, place the bread cubes in a large bowl and add the contents of the pot to the bowl; stir.
Pour the broth/egg mixture over the bread cubes and stir. The bread should be moist but not soggy. If it is still very dry, stir in a little more broth, until all of the bread cubes are lightly moistened. If you like your stuffing more moist, you will want to add more broth than the 1½ cups listed in the recipe, as this amount yields a drier stuffing.
Pour the mixture into the prepared baking dish and spread into an even layer. Cover the dish with foil and bake for 30 minutes. Then uncover and continue baking for 15-25 more minutes, or until stuffing is browned on top and at least 160° F in the center when tested with an instant read thermometer.