Place the sliced potatoes in a large pot and cover with cold water. Add a generous pinch of salt. Bring the water to a boil, then reduce to a gentle simmer. Cook the potatoes for 5 to 7 minutes, or until just tender but not fully cooked through. Drain and set aside to cool slightly.

In a large skillet, melt 2 tablespoons of butter with 1 tablespoon of olive oil over medium heat. Add the sliced onions and cook, stirring occasionally, for approximately 15 to 20 minutes, or until deeply golden and caramelized. Season lightly with salt. Once caramelized, remove the onions from the skillet and set aside.

In the same skillet, add the remaining 2 tablespoons of butter and 1 tablespoon of olive oil. Arrange the parboiled potato slices in a single layer, working in batches if necessary to avoid overcrowding. Season with salt, black pepper, and thyme. Cook each batch for 5 to 7 minutes per side, turning gently, until the potatoes are golden brown and crisp. Transfer each batch to a plate once done.

Return all the cooked potatoes to the skillet and add the caramelized onions. Toss gently to combine. If the mixture appears dry, add a small amount of chicken or vegetable stock and stir gently to incorporate. Adjust seasoning with additional salt and pepper if needed.

Sprinkle the dish with freshly chopped parsley before serving. Serve immediately while hot, ideally as an accompaniment to roasted meats, poultry, or seafood.