Preheat the oven to 375 degrees F.
Pound out the chicken cutlets until they are paper thin. Sprinkle them with the garlic powder, onion powder and salt and pepper. Heat the olive oil in a pan over medium heat and saute the chicken for 3 to 4 minutes on each side. Set these aside to cool.
To make the cheese sauce: In a medium saucepan, heat the butter over medium-low heat until melted. Add in the flour and whisk until the mixture is smooth. Cook this over medium heat until the mixture is a light golden color.
Meanwhile, heat the milk in a separate pan but do not allow it to come to a boil. Add the milk to the butter and flour mixture one cup at a time, whisking continuously until it is very smooth. Once all the milk is added in, bring this to a low boil and cook it for 10 more minutes, stirring constantly. Add in the Cheddar and fontina and continue stirring until they are melted. Remove the sauce from the heat and add in the cayenne and black pepper. Taste the sauce before adding salt as the cheeses are salty themselves. Set the sauce aside to cool and thicken.
Prepare an ice water bath. Steam the head of broccoli in a steamer until it is crisp tender. Then immediately place it in the ice bath. Remove the florets and break them down to a uniformly small size. Julienne the stems of the broccoli. In a large bowl, combine the broccoli with the cheese sauce.
Roll out the pizza dough on a flat surface in the shape of a rectangle, approximately 11 by 17 inches in dimension.
Lay the chicken cutlets over the dough, overlapping them to prevent the cheese sauce from seeping through the bread and making it mushy. Spoon the broccoli and cheese mixture over the bed of chicken. Roll the dough up, tucking in the ends as you would a burrito. Continue rolling and seal the end of the roll with the egg wash. Cover the entire roll with the remaining egg wash as well.
Place the garbage bread roll on a baking sheet and bake, checking frequently, until the crust is firm and lightly browned and the dough is cooked through, 35 to 40 minutes. Cut the bread into 2-inch slices and serve.