Heat the olive oil in a large skillet over medium heat. Add the shallots, garlic and artichoke hearts and sautee until the artichoke begins to brown (about 8-10 minutes). Remove from the heat, stir in the herbs and let cool (about 10 minutes).
Whisk milk, salt, pepper and eggs together in a large bowl. Add the Parmesan cheese and toss in the bread until well combined.
Preheat the oven to 375F. Mix the artichoke mixture into the bread mixture and let sit for 20 minutes.
Grease an 8" square baking dish and pour half of the mixture into the dish. Next layer with half of the goat cheese. Repeat until all ingredients are used.
Bake at 375F until browned and bubbly (about 45-50 minutes).