In a saucepan over a medium to high heat, add the onions, butter and oil. Stir together and turn to low heat, covering with a lid or a cartouche. Cook very slowly for 30 minutes, until onions are completely softened and sweet.
Next, turn back to medium to high heat and cook until the onions are golden-brown. Stir occasionally so nothing catches on the bottom. Make sure to caramelize the onions to a deep golden color, as it will impart flavor to the soup.
Add the garlic and cook for a minute, followed by white wine and cook until the liquid has reduced slightly.
Add the thyme, pour in the stock and bring to the boil. Stir together and reduce the heat slightly. Cook for about 15 minutes, or until the stock has reduced by 2/3rds and the mixture is thickened.
Spray a mini-muffin tin with non-stick cooking spray. Gently place a wonton wrapper into each hole. Spoon about a tablespoon of the onion mixture into each wonton. Top with the cheese and bake for about 10 minutes or until golden brown. Garnish with more thyme if you want.