Line slow cooker with foil collar and spray with vegetable oil spray.
Using food processor fitted with 1/4-inch slicing disk, slice potatoes, carrots, and parsnips.
Microwave sliced vegetables and 2 T cream in covered bowl, stirring occasionally, until vegetables are almost tender, 6-8 minutes.
In large bowl, microwave remaining cream, broth, cornstarch, butter, garlic, salt, pepper, and thyme, stirring occasionally, until thickened, about 1 minute.
Slowly whisk in 3/4 c cheddar until evenly melted.
Spread half of sauce in prepared slow cooker.
Arrange vegetable mixer over sauce into even thickness and press gently to compress layers.
Spread remaining sauce over top.
Cover and cook until vegetables are tender, 5-6 hours on LOW or 3-4 hours on HIGH.
Remove foil collar.
Sprinkle with remaining ½ c cheddar and let sit until cheese is melted and casserole is cooled slightly, about 20 minutes; serve.
**To make a foil collar—fold sheets of heavy-duty foil until you have a six-layered foil rectangle that measures roughly 16 inches long by 4 inches wide for a large slow cooker or 12 by 4 inches for a small slow cooker; then press the collar into the back side of the slow cooker insert; the food will help hold the collar in place during cooking and the collar will prevent the food from cooking unevenly.