Spread baguette slices on a baking sheet. In a skillet, melt the butter at medium heat. Brush the slices with about 1 tablespoon of melted butter. Cook under the preheated grill for about 4 minutes or until the slices are golden and crispy (flip at mid-cooking). Set aside.
Meanwhile, in the skillet, add shallots and garlic. Cook, stirring, for 3 minutes or until softened. Add mushrooms, thyme, salt, pepper and cook while stirring for about 7 minutes or until mushrooms are golden and liquid has evaporated. Add parsley and stir.
When ready to serve, spread about 1 tablespoon of the mushroom mixture on each crostini and sprinkle with oil. Serve hot.