Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish.

In a large skillet, heat olive oil or butter over medium-low heat. Add the sliced onions and a pinch of salt. Cook, stirring occasionally, until deeply caramelized and golden brown — about 25–30 minutes. Near the end, stir in the minced garlic for 1–2 minutes until fragrant.

While onions caramelize, thinly slice the potatoes using a mandoline or sharp knife for even layers. Pat slices dry to remove excess starch.

In a medium bowl, combine the broth, sour cream or yogurt, thyme, and flour (if using). Season with salt and pepper.

Layer half of the potato slices in the prepared dish, slightly overlapping. Spread half of the caramelized onions over the potatoes, sprinkle half of the cheese, and pour half of the sauce mixture over the layers. Repeat with remaining potatoes, onions, cheese, and sauce.

Cover the dish with foil and bake for 35 minutes. Remove foil and bake for an additional 10–20 minutes until the top is golden and potatoes are tender when pierced with a fork.

Let rest for 10 minutes before slicing. Sprinkle with chopped chives or parsley and serve warm.