Heat the olive oil in a large skillet over medium heat.
Add the wild mushrooms and cook until they release their liquid and begin to brown, about 8 minutes.
Season with salt and pepper, then add the thyme sprigs and cook for one more minute.
Remove the skillet from the heat and let the mushrooms cool for a few minutes.
Place the mushrooms in the center of a large charcuterie board.
Scatter the blackberries and dried cherries around the mushrooms.
Arrange the brie slices, cheddar cubes, and salami slices in separate sections on the board.
Fill remaining spaces with baguette rounds and walnuts.