Heat olive oil in a large saucepan over medium heat. Whisk in flour; cook 1 minute.
Whisk in half-and-half, 2 percent milk, garlic, salt and dried thyme. Add potatoes and bring to simmer. Cook 1 minute.
Spoon into greased 8 x 8 x 2-inch baking dish and cover with foil. Bake at 375 degrees F for 40 minutes. Uncover and bake additional 10 minutes. Cool slightly. Garnish with chopped parsley.