Preheat the oven to 450 degrees F. Line a rimmed baking sheet pan with foil and spray with cooking spray. Slice the very bottom off of each potato so they lay flat on a cutting board. Make a series of 1/8-inch slices along the top of each potato, stopping ½ inch from the bottom so you don't slice all the way through the potatoes. You can place two wooden chopsticks or utensil handles along the sides of the potato to help prevent you from slicing all the way through – but take care on the tapered ends because they are above the chopsticks. Transfer the potatoes to the prepared baking sheet and drizzle with 3-4 tablespoons olive oil. Use your hands to rub all sides of the potatoes thoroughly with the oil.
Bake the potatoes for 50 to 60 minutes OR until the center of the potatoes are tender. Near the end of the baking time, mix together all of the Garlic Thyme Butter ingredients in a medium bowl. Once the potatoes are tender, remove the pan from the oven. Brush the Garlic Thyme Butter in between every slice (it's okay if some butter drips on the baking sheet). Insert the cheese slices in between every other cut or every few cuts of potato (if using 8 ounces cheese) or in between about every cut if using 16 ounces of cheese. Return the potatoes to the oven and bake for an additional 3-5 minutes or until the cheese is melted.
Garnish with additional chopped chives if desired. Serve immediately.