Step 1: Caramelize the onions. Melt the butter with the oil in a large skillet over medium heat. Add the onions and salt and cook for 25 to 30 minutes, stirring often, until deep golden brown. Lower the heat if they start to burn.
Step 2: Build the sauce. Stir in the garlic for 1 minute, then sprinkle in the flour and stir for 1 minute. Pour in the wine and scrape up the browned bits. Add the broth, Worcestershire, and thyme and simmer for 5 minutes, until slightly thickened.
Step 3: Assemble. Heat the oven to 375 degrees F. Season the chicken with the salt and pepper and spread it in a 9x13 inch dish. Pour the onion sauce over the chicken.
Step 4: Bake covered. Cover with foil and bake for 25 minutes, until the chicken reaches 165°F (74°C) in the center of a piece.
Step 5: Top and broil. Remove the foil, lay the baguette slices over the top, and cover with the Gruyère. Bake 8 to 10 minutes, then broil 1 to 2 minutes, until the cheese is golden and bubbling. Watch closely.
Step 6: Rest and serve. Rest for 5 minutes, then sprinkle with parsley.
