Toast bread in a shallow baking pan in middle of oven, stirring once or twice, until crisp, about 7 minutes.
Peel artichokes with a vegetable peeler and cut into 1-inch pieces, then simmer in milk and water in a 3-quart heavy saucepan, partially covered (be careful not to let it boil over), stirring occasionally, until artichokes are very tender, about 15 minutes.
Purée artichokes with cooking liquid, salt, and pepper in 2 batches in a blender until smooth (use caution when blending hot liquids). Transfer purée to same saucepan and thin with additional water if necessary. Heat soup over moderate heat, stirring, until hot. Serve topped with croutons and parsley.
