Sauté the onions: In a large saucepan, melt 1 tablespoon of butter over medium heat. Add the sliced onions and cook until they are softened and caramelized, stirring occasionally, about 20-25 minutes.
Add the garlic and thyme: Add the minced garlic and dried thyme to the saucepan and cook for 1 minute, stirring constantly.
Add the chicken broth: Pour in the chicken broth and bring the mixture to a boil.
Add the rice: Stir in the uncooked rice and reduce the heat to low. Cover the saucepan and simmer for 18-20 minutes, or until the rice is tender and the liquid has been absorbed.
Season with salt and pepper: Season the rice mixture with salt and pepper to taste.
Top with Gruyère cheese and parsley: If using, sprinkle the grated Gruyère cheese and chopped parsley over the top of the rice mixture.