Preheat oven to 350 F. In a food processor, place egg, 1/3 of soup, onion, garlic powder & salt & pulse for 30 seconds. Add half of the milk, spinach, mustard, bread, thyme & Parmesan. Blend another 30 seconds.
Lay ham slices on work space and divide filling evenly among them. Arrange filled ham rolls in a shallow baking dish. Combine remaining soup & milk; spoon evenly over rolls. Bake, covered for 15 minutes, remove foil & bake 10 more minutes or until bubbly & filling is cooked through. If preferred, garnish with dried parsley.