In a large skillet, melt 2 tablespoons of unsalted butter and 2 tablespoons of olive oil over medium-low heat. Add thinly sliced yellow onions and cook them gently, stirring occasionally, for about 30-40 minutes until they are deeply golden and caramelized.

Once the onions are caramelized, add 3 cloves of minced garlic, 1 tablespoon of fresh thyme, and season with salt and freshly ground black pepper. Cook for another minute until the garlic is fragrant. Deglaze the pan with 1 tablespoon of balsamic vinegar.

Stir in 1 cup of dry orzo pasta to the onion mixture, then pour in 3 cups of beef broth. Bring to a simmer and cook uncovered for about 8-10 minutes, stirring occasionally, until the orzo is nearly tender and most of the liquid is absorbed.

Reduce heat to low, mix in 1 cup of heavy cream and half of the Gruyère, mozzarella, and Parmesan cheeses. Stir continuously until the cheeses are fully melted and the sauce becomes creamy.

Transfer the orzo mixture into a greased baking dish and sprinkle the remaining cheeses generously on top. Preheat your oven to 400°F (204°C) and bake for 10-15 minutes, or until the top is bubbly and golden brown.

Once baked, remove from the oven and allow to cool for 5-10 minutes. Garnish with freshly chopped parsley or chives before serving.