Preheat your oven to 400°F (200°C) and lightly grease a large baking sheet.

Scrub the potatoes clean, pat them dry, and prick each one several times with a fork.

Place the potatoes on the prepared baking sheet and bake for 55–60 minutes, or until tender when pierced with a fork.

Remove from the oven and set aside to cool slightly. Keep the oven on for the final bake.

While the potatoes bake, heat the olive oil and butter in a large skillet over medium heat.

Add the sliced onions and cook slowly, stirring often, until they turn a deep golden brown — about 20 minutes.

Add the sliced mushrooms to the skillet with the onions and continue cooking for 6–8 minutes, stirring occasionally, until the mushrooms are tender and lightly browned.

Stir in the minced thyme and cook for another minute to release the herb’s aroma.

Pour in the beef broth and scrape up any browned bits from the pan using a wooden spoon.

Let the mixture simmer for 3–5 minutes, until the broth reduces slightly and forms a glossy coating on the onions and mushrooms.

Season generously with salt and freshly ground black pepper to taste.

Remove from heat and let the filling cool slightly while preparing the potatoes.

Once the baked potatoes are cool enough to handle, carefully slice each one lengthwise down the center.

Use a fork to gently fluff the insides and create space for the filling.

Spoon the warm onion-and-mushroom mixture evenly into each potato.

Sprinkle the tops generously with shredded Swiss or Gruyère cheese.

Return the filled potatoes to the oven and bake for 15–20 minutes, or until the cheese is melted and the filling is bubbling.

For a beautifully browned top, broil for 2–3 minutes, watching closely until the cheese turns golden and slightly crisp.

Let the potatoes rest for about 5 minutes before serving.