Let's cook.
Pat the chicken breasts dry with paper towels and season them with 0.5 teaspoon of salt and 0.25 teaspoon of black pepper.
Heat 1 tablespoon of olive oil in a large oven-safe skillet over medium-high heat. Sear the chicken breasts for 3-4 minutes per side, until golden brown. Remove chicken from the skillet and set aside.
Reduce heat to medium. Add the remaining 1 tablespoon of olive oil to the skillet, then add the sliced onions and the remaining 0.5 teaspoon of salt. Cook, stirring occasionally, for 15-20 minutes, until the onions are deeply caramelized and tender.
Add the minced garlic to the skillet and cook for 1 minute until fragrant. Pour in the dry white wine and scrape up any browned bits from the bottom of the skillet. Let it simmer for 2 minutes until slightly reduced.
Stir in the beef broth and bring the mixture to a gentle simmer. Return the seared chicken breasts to the skillet, nestling them into the onion mixture.
Sprinkle the shredded Gruyère cheese evenly over the chicken and onions. Transfer the skillet to a preheated oven at 375°F (190°C) and bake for 10-12 minutes, or until the chicken is cooked through (internal temperature of 165°F / 74°C) and the cheese is bubbly and golden.
Carefully remove the skillet from the oven. Let it rest for 5 minutes before serving.
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