Preheat the oven to 375°F (190°C).

In a large skillet over medium heat, melt 2 tablespoons of butter with olive oil. Add the sliced onions, sugar, salt, and pepper. Cook while stirring occasionally for about 25 minutes until they are deep golden brown and perfectly caramelized.

Meanwhile, bring a pot of salted water to a boil. Add the gnocchi and cook until they float, usually around 2-3 minutes. Drain and set aside.

In the same skillet, melt the remaining 2 tablespoons of butter over medium heat, then add the minced garlic and sauté for about 30 seconds until fragrant.

Stir in the flour and cook for 1 minute.

Gradually whisk in the beef broth and milk, adding the thyme leaves. Simmer until the sauce thickens, about 3-5 minutes.

Stir the cooked gnocchi and half of the caramelized onions into the sauce, coating them well.

Transfer the mixture into a baking dish and sprinkle with Gruyere, Parmesan, and mozzarella cheeses. Top with the remaining caramelized onions.

Bake for 15-20 minutes until the cheese is bubbly and golden. Let it rest for 5 minutes before serving.