Preheat the oven to 375°F / 190°C / Gas Mark 5, no fan (if you have a convection oven reduce the temperature by about 20° or follow the manufacturer's instructions).
Cut the button mushrooms into 1/4-1/3 inch (5-7mm) slices. Chanterelle mushrooms: leave small mushrooms whole, cut medium mushrooms into 2 parts, and large mushrooms into 3-4 parts. Don't cut the mushroom too thinly.
14 oz (400g) mushrooms
Cut the shallot into slices, finely chop the garlic.
2 shallots, 3 cloves garlic
Heat butter in a large frying pan over medium-low heat. When hot add the onions and thyme, cook for a couple of minutes, until the onion is soft. Add the garlic and cook for 30 seconds, stirring.
1 tablespoon butter, 2 teaspoons dried thyme
Transfer the onions with garlic to a plate.
Add oil to the pan and increase the heat to the highest setting. Add mushrooms in an even layer, starting with button mushrooms (chanterelle mushrooms should be on top of button mushrooms). Cook without stirring for 1-2 minutes then add the vinegar and cook, stirring, for about 4-8 minutes (depending on how powerful your stovetop is) until the mushrooms have reduced their volume in half and all the liquid is evaporated. Don't stir the mushrooms for about a minute when almost all liquid is evaporated, letting the mushrooms brown a little.
1 tablespoon oil, 1 tablespoon balsamic vinegar
Add the onions with garlic back to the pan, stir with the mushrooms. Season the mushrooms and onions with salt and pepper. Transfer to a plate and leave to cool slightly.