Pour 1 tbsp oil into a large heavy based frying pan, add the whole garlic cloves then set the pan over a medium heat. When the oil is hot fry the pheasant breasts for 2-3 minutes each side until lightly browned and just cooked through. Transfer them to a board, leave to rest for a few minutes, then slice.
Heat the remaining oil to the pan, add the mushrooms and fry for 1-2 minutes. Pour in the wine and allow to bubble rapidly for a second or two. Remove from the heat. Add the red onion and thyme. Season.