Preheat oven to 200º.
Cube bread into equal sized pieces. Spread on a large sheet pan and place on the middle rack of the oven for 30 minutes. Remove from oven and let cool. Turn oven to 350º.
Heat 3 Tbsp unsalted butter over medium heat in a large skillet.
Sauté onion, carrots, celery and garlic until softened; about 5 minutes.
Add parsley, rosemary, thyme and marjoram to the skillet. Stir often, for another 2 minutes.
Place bread cubes in a large bowl.
Pour sautéed vegetables over the bread and stir to coat.
Add the egg and black pepper to broth, and whisk until egg has become fully emulsified into the broth. Pour mixture into bread bowl, and mix with clean hands to completely coat the bread.
Line an 8x8" baking dish with parchment paper. (Cut two pieces of parchment that are 12"x8" and lay them so they cross each other in the pan.) To keep moisture in, cover the pan with foil.
Bake for 30 minutes, remove foil, and bake another 10 minutes.