Preheat oven to 350°F.
Pat chicken breast dry with paper towels to remove any moisture from packing. Generously season both sides with salt, pepper, and Italian seasoning.
Heat oil over medium heat in a high sided, oven-safe skillet. When oil begins to shimmer, add chicken breast. Brown on each side, 4-6 minutes. Remove to a plate and set aside.
Add 2 tablespoons of butter to the same skillet and melt. Add the onions to the melted butter and cook, stirring until the onions begin to soften. Add 1/4 teaspoon salt.
Reduce heat to medium-low (lower heat as needed so onions don't burn) and continue to cook, stirring often, until the onions are soft but not mushy. Sprinkle the onions with flour and toss to coat.
Add the beef and chicken broth, sherry and thyme to the onions. Bring to a boil, scraping up any brown bits on the bottom of the pan. Boil for 1-2 minutes or until sauce is thick.
Add chicken back to pan and nestle into onion mixture. Spoon some sauce over the chicken. Top with Gruyere.
Place skillet in preheated oven and cook until the cheese is melted and bubbly. It's better not to brown the cheese, just allow it to melt. Adjust seasoning if need. Spoon a little onion mixture and sauce over chicken, top with fresh thyme or chopped parsley(optional) and Serve.