In 4-quart saucepan or 5-quart Dutch oven, place potatoes; add enough water just to cover potatoes. Heat to boiling. Reduce heat; cover and simmer 20 to 30 minutes or until potatoes are tender when pierced with a fork. Drain.
Heat oven to 350°F. Spray 2- to 3-quart casserole with cooking spray. In 1-quart saucepan, heat milk, butter, salt and pepper over medium heat, stirring occasionally, until butter is melted. Measure out 1/4 cup milk mixture; set aside.
To potatoes, gradually add remaining milk mixture, cubed cheese and thyme, mashing with potato masher or electric mixer on medium speed until light and fluffy. Spoon potatoes into casserole. (Potatoes can be covered and refrigerated up to 24 hours at this point.)
Pour reserved 1/4 cup milk mixture over potatoes. Bake uncovered 40 to 45 minutes or until potatoes are hot. Stir potatoes before serving.