Preheat the oven to 350 degrees . Grease a large, ovenproof skillet. In a bowl, whisk together the milk and olive oil. Stir in the bread cubes and let stand until the liquid is absorbed.
Meanwhile, in a bowl, combine the cream, eggs, garlic, pepper, salt and nutmeg. In another bowl, crumble the goat cheese; add the parmesan, fontina, sage and thyme.
Place half of the bread mixture in the prepared skillet. Top with half each of the ham, artichoke hearts and herb-cheese mixture. Pour half of the egg mixture over the layers. Repeat with the remaining bread, ham, artichoke hearts, herb-cheese mixture and egg mixture. Bake until firm in the center and brown around the edges, about 1 hour.