In a large pan, heat the butter and oil over medium heat. When melted add the onions, thyme, salt and pepper. Cook slowly until it starts to caramelize into a golden brown.
Add the garlic and saute until aromatic. Pour in the white wine to deglaze the pan and stir through. Cook for 1 minute. Add the broth and cook down with the onions until really nicely caramelized and jammy. Set aside to cool.
In a bowl, mix together cooled onions, 100g mayonnaise and, gruyere cheese.
Preheat oven to 200ºC. Line a sheet pan with foil.
Make a slit in each of the chicken breasts on the side to make a pocket.
Stuff each pocket with the onion mixture and press to close.
Brush each chicken breast all over liberally with Garlic and Onion Mayonnaise. Coat in panko bread crumbs, pressing to adhere.
Transfer the chicken breasts to the prepared sheet pan. Bake for 25-30 minutes until golden brown and cooked through.