While potatoes dry, heat half the butter and oil in a large skillet (cast iron preferred) over medium heat. Add the sliced onions and cook, stirring occasionally, until deeply caramelized and golden brown (about 15-20 minutes).

Stir the fresh thyme into the onions, then deglaze the pan with the dry sherry, scraping up any browned bits from the bottom. Cook for 1 minute until the liquid evaporates. Remove the onion mixture from the pan and set aside.

Wipe out the skillet if necessary, then add the remaining butter and oil over medium-high heat. Add the parboiled potato slices in a single layer (work in batches if necessary) and fry until crispy and golden brown on both sides.

Return the caramelized onions to the pan and toss gently to combine with the crispy potatoes. Season with salt and pepper.

Sprinkle the shredded Gruyère cheese evenly over the potato and onion mixture.

Place the skillet under a broiler for 2-3 minutes, or until the cheese is melted, bubbly, and slightly browned.

Remove from heat, garnish with fresh chopped parsley, and serve immediately.