Preheat the oven to 200°C (400°F) or 180°C (350°F) for fan-forced ovens.
In a small saucepan over medium heat, combine the pure cream, bruised garlic cloves, and thyme sprigs. Bring the mixture to a gentle simmer for about 6 minutes, allowing the flavors to infuse. Remove from heat, season generously with salt and pepper, and set aside to steep while preparing the potatoes.
Place one potato half, cut-side down, on a chopping board. Position a bamboo skewer on each side to act as a guide. Using a sharp knife, carefully make thin, even slices along the potato, about 3 mm apart, ensuring not to cut all the way through. Repeat this process with the remaining potato halves. The skewers will prevent the knife from slicing completely through.
Lightly grease a 4 cm-deep roasting pan measuring approximately 25 x 35 cm (base). Arrange the potatoes cut-side down in a single layer within the prepared pan. Sprinkle evenly with half of the grated cheddar and half of the parmesan. Strain the infused cream mixture through a fine sieve into a jug, discarding the solids, and pour the warm liquid evenly over the potatoes.
Cover the pan tightly with foil and bake for 40 minutes, or until the potatoes are just tender and beginning to separate slightly between the slices. Remove the foil and scatter the remaining cheddar and parmesan over the top. Return to the oven and bake, uncovered, for an additional 40 minutes, or until the potatoes are golden, crisp at the edges, and soft on the inside.
Once baked, garnish with extra thyme sprigs and a final sprinkle of salt and pepper. Serve hot as a stunning side dish that pairs beautifully with roasted meats or as a rich centerpiece for any comforting meal.