Preheat oven to 350 F. On 2 cookie sheets, toast the bread cubes for 15 minutes, or until the bread is golden brown. Transfer to a very large mixer bowl. Bone the chicken and very finely chop the meat, discarding the skin. (I do this in the food processor while chicken is still warm.) Add the chopped vegetables and chicken meat to the bread, along with the seasonings. Toss. In a medium bowl, beat the eggs; add the evaporated milk and broth. Pour over the bread mixture and blend. The mixture will be quite moist. Allow to stand 1 hour. Preheat oven to 350 F. Transfer the dressing to an oiled 3 quart glass casserole that is 10 inches in diameter and 3 inches deep (at this point, dressing can be frozen for future use; thaw before baking.) Bake dressing for 2 hours, or until the center of the dressing puffs up and is golden brown on top.