Clean the mushrooms, possibly rubbing with kitchen paper. Cut larger mushrooms in half. Peel and finely dice the shallot. Wash the thyme, shake dry and pluck the leaves. Coarsely grate the cheese. Heat oil in a pan.
Stir-fry the mushrooms and shallot briefly while stirring. Add thyme. Season with salt and pepper.
Preheat the oven grill. Line a baking tray with baking paper. Place baguette slices on top. Roast on the top rack for about 2 minutes until golden brown, turning after about 1 minute. Take out. Halve the garlic clove.
Rub one side of each slice of bread with the cut surface of the garlic clove. Use the rest of the garlic for other purposes.
Spread the mushroom mixture on the baguette slices. Sprinkle the cheese on top and bake under the grill for about 1 minute.