Preheat your oven to 375°F (190°C) and lightly grease a small oven-safe baking dish.
Slice the Yukon Gold potato into very thin rounds, approximately 1/8-inch thick, using a mandoline or sharp knife.
Thinly slice the chicken breast into bite-sized strips or rounds to match the potato thickness.
In a medium bowl, whisk together the Greek yogurt, chicken broth, minced garlic, thyme, rosemary, salt, and pepper until smooth.
Layer half of the potato slices in the bottom of the dish, followed by all of the chicken strips, and then the remaining potato slices.
Pour the yogurt mixture evenly over the layers, pressing down slightly to ensure the sauce seeps between the slices.
Cover the dish with foil and bake for 30 minutes.
Remove the foil, sprinkle the parmesan cheese over the top, and bake for another 15-20 minutes until the potatoes are tender and the top is golden brown.