In an oven-safe skillet, combine unsalted butter and olive oil over medium-low heat. Once melted, add the sliced yellow onions, stirring often for about 25–30 minutes until they turn golden brown.

Stir in the minced garlic, fresh thyme, salt, and black pepper, cooking for about 1 minute. Then, deglaze the skillet by pouring in the balsamic vinegar, scraping up any golden bits stuck to the bottom.

Add the dry orzo pasta directly into the skillet and pour in the beef broth, stirring to combine. Allow the mixture to simmer uncovered for 8–10 minutes until the orzo is tender and much of the liquid has been absorbed.

Stir in half of the Gruyère and mozzarella cheese until melted, then top with the remaining cheeses.

Preheat your oven to 400°F (200°C). Carefully transfer the skillet to the oven and bake for 10–15 minutes until the top is bubbly and golden brown.

Remove from the oven and allow to cool for a few minutes. Garnish with chopped parsley or chives before serving.