Preheat the oven to 375°. In a large skillet, heat 2 tablespoons of the olive oil. Add the diced leeks and cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Add the shiitake and cook, stirring often, until their liquid has evaporated, about 5 minutes. Stir in the garlic and the thyme and cook for 2 minutes. Season with salt and pepper and transfer to a medium bowl.