Bring large pot of water to boiling. Peel potatoes; thinly slice; place slices in bowl of cold water as you slice. Drop drained slices into boiling water; boil 3 minutes. Drain; reserve.

Heat oven to 375. Coat inside of 12x7x2-inch or other 2.5-3 quart baking dish with nonstick cooking spray.

Stir together half cup milk and the flour in medium-size saucepan until smooth. Stir in remaining 1 cup milk, the half and half, water, vegetable broth powder, thyme, salt and pepper; cook, stirring, over medium heat until sauce thickens and bubbles, about 3 minutes.

Spoon one-third of potatoes into prepared casserole. Sprinkle with half of the ham and green onion. Spoon on one-third of sauce. Repeat layers. Top layer should be potatoes with remaining sauce poured over all.

Bake, covered, in 375 oven for 30 minutes. Sprinkle cheese over top and sut with paprika if desired. Bake, uncovered, 15 minutes or until lightly browned. Let stand 10 minutes before serving.