Preparation Preheat oven to 350°F. Butter 13 x 9 x 2-inch glass baking dish. Whisk milk and oil in large bowl. Stir in bread. Let stand until liquid is absorbed, about 10 minutes. Whisk cream and next 5 ingredients in another large bowl to blend. Add goat cheese. Mix herbs in small bowl to blend. Place half of bread mixture in prepared dish. Top with half of ham, artichoke hearts, herbs, and cheeses. Pour half of cream mixture over. Repeat layering with remaining bread, ham, artichoke hearts, herbs, cheeses, and cream mixture. (Can be made 1 day ahead. Cover; chill.) Bake uncovered until firm in center and brown around edges, about 1 hour.
Preparation Preheat oven to 350°F. Butter 13 x 9 x 2-inch glass baking dish. Whisk milk and oil in large bowl. Stir in bread. Let stand until liquid is absorbed, about 10 minutes. Whisk cream and next 5 ingredients in another large bowl to blend. Add goat cheese. Mix herbs in small bowl to blend. Place half of bread mixture in prepared dish. Top with half of ham, artichoke hearts, herbs, and cheeses. Pour half of cream mixture over. Repeat layering with remaining bread, ham, artichoke hearts, herbs, cheeses, and cream mixture. (Can be made 1 day ahead. Cover; chill.) Bake uncovered until firm in center and brown around edges, about 1 hour.