Preheat oven to 400°F with convection, or 425°F without.
Pour the tomatoes into a large mixing bowl and crush them by hand until they have a rustic, chunky texture.
Tear the bread into roughly 1-to-1½-inch pieces. Add the bread to the bowl, along with the melted butter, sugar, salt, and black pepper. Mix it well with your hands, until all of the tomato juice has been absorbed into the bread.
Grease a 12-inch skillet with the room temperature butter, making sure to get both bottom and walls. Dump in the bread mixture. Shape it into a relatively even layer, touching the walls of the skillet as much as possible to create a crust, but not pressing it or compacting it. Place it in the center of the oven. Bake until it is set, and rustically charred, making sure that the sides of the pudding are caramelized, about 1 hour. Once it is cooked, let it rest at least 15 minutes.
Serve it garnished with whole anchovy filets and more black pepper.