Combine 1/2 cup mayonnaise and next 3 ingredients in a saucepan. Gradually add milk, and cook, stirring constantly, over medium-low heat 8 to 10 minutes or until thickened. Remove from heat.
Add Cheddar cheese and next 3 ingredients, stirring until cheese melts and is well blended.
Place half of potato slices evenly in a lightly greased 11- x 7-inch baking dish; pour half of cheese mixture over potatoes. Repeat layers with remaining half of potato slices and cheese mixture. Sprinkle evenly with Parmesan cheese.
Bake, covered, at 350° for 1 hour. Uncover and bake 30 more minutes or until potatoes are golden brown and fork tender.