Place shredded potato into a large bowl of cold water and allow potatoes to sit for about 1 hour.
Drain water from potatoes and squeeze out as much excess water as possible.
Place shredded and squeezed potatoes into a clean mixing bowl and toss together with cheese, thyme, salt, and pepper.
Place a large cast iron skillet over medium heat and melt 1 tablespoon butter.
Scoop 3 to 4 (½ cup scoops) of the mixture and place into the hot skillet, about 1 inch a part, pressing down on the potato pile with the back of a spatula to flatten. Fry hash browns for 4 to 5 minutes on each side or until browned and crispy.
Remove from heat and transfer to baking sheet lined with a cooling rack. Lightly season with salt.
Repeat steps 5 and 6 until all the potato mixture has been used.
Transfer hash browns to a platter and top with more minced thyme. Serve.