Preheat convection oven to 375°F.
Prepare the Pioneer® Old Fashioned Biscuit Gravy Mix according to package instructions. Reserve 3 quarts of the gravy for another use and set aside remaining 1 quart.
Slice the potatoes very thinly, lengthwise. Do not peel potatoes. Use a food processor with less than 1/8-inch thin blade setting or a mandolin to slice potatoes. Place potatoes in a bowl with room temperature water while slicing remaining potatoes.
Mix 3 cups of milk with 1 quart of remaining gravy, whisk to combine.
Drain potatoes from the water, then place back in bowl. Add gravy and milk mixture. Season with salt and pepper as desired. Add thyme to mixture.
Prepare two half hotel pans (2-inch) with butter, smearing on all sides and bottoms of both pans.
Layer pan with potatoes, placing them in a shingle-like pattern across the bottom of the pan. When a layer is complete, sprinkle a small amount of cheese on top of layer. Make 3–4 layers in pan until you reach just below the top of the pan. Repeat with other pan.
When both pans are complete, pour remaining gravy and milk mixture on top of both pans equally. Top each pan with remaining small amount of cheese.
Cover each pan with foil and bake for 45 minutes, then uncover and bake an additional 30 minutes to achieve browning on top. Let rest for 10–15 minutes, then serve.