Preheat the grill to 375 degrees. Meanwhile, peel the potatoes before thinly slicing them with a mandolin (I went with the thinnest setting, but adjusted to preference). Place the sliced potatoes in a bucket with water for ~20 minutes.
Mix the butter, garlic, and herb paste until well combined. Using a pastry brush, apply the butter mix to a cast iron skillet, then add a piece of parchment paper.
Next, pour out the water the potatoes were soaking in and pat dry with a paper towel. Begin to layer the potatoes in the cast iron skillet, working your way from outside in until the cast iron skillet is completely covered. Brush the potatoes with the butter mix and add a pinch of salt. Repeat this step until all potato slices have been used, ~8-10 layers. Press a piece of parchment paper firmly on the potatoes, then add the skillet to the grill.
Cook the potatoes on the grill until tender and the butter is bubbling, ~1 hour. At this point, remove the skillet from the grill. Place a plate over the potatoes (this will help prevent them from curling up). Allow the skillet to cool at room temperature, then refrigerate it overnight.
When you're ready to cook the potatoes the next day, preheat the grill to 500 degrees or high setting (you could also do this final step on the stove). Take out the skillet and remove the potatoes using the parchment paper—the potatoes should resemble a pie at this point. Slice the potato into 6-8 pieces.
Add the skillet pack to the grill with three potato slices. Allow the potatoes to cook until golden brown, flipping as needed. Repeat with the remaining potato slices.
Once the potatoes are finished, garnish with flaky salt & thyme. Serve & enjoy!