Preheat the oven to 425.
Prep your potatoes, one at a time, by placing them between a pair of chopsticks. With a very sharp knife, cut all the way down towards the chopsticks, at 1/8th-inch intervals. Use the knuckles of your left hand as a guide as you inch along. Continue until you've done this to every potato.
In a large cast-iron skillet, toss the potatoes with the olive oil, a big sprinkling of kosher salt (at least 1 tablespoon) and freshly ground black pepper. Be sure to get the oil and salt in between the layers of potato. Insert garlic slices in between the slits of as many potatoes as you can. Layer the thyme on top.
Cover with foil and bake for 20 to 25 minutes, or until the potatoes are just tender. At this stage you can cool the potatoes in the pan and refrigerate, still covered with foil, until ready to finish the next day.
Remove the foil and place the potatoes back in the oven for 40 to 45 minutes, until deep golden brown all over and crispy on the top. Remove from the oven and let cool slightly before serving.
