In a large skillet, heat 2 tablespoons of the oil. Add the shiitake and season with salt and pepper. Cover and cook over moderate heat, stirring, until tender and starting to brown, about 7 minutes. Transfer to a bowl.
Heat 1 tablespoon of the oil in the skillet. Add the mixed mushrooms and cook over moderately high heat until any liquid has evaporated and the mushrooms start to brown, 5 minutes. Add the onion and remaining 1 tablespoon of oil; season with salt and pepper. Cover and cook over moderate heat, stirring, until the onion is softened, 5 minutes. Add the garlic, cover and cook over low heat, stirring a few times, until fragrant, 2 minutes. Add the wine and cook for 2 minutes. Add the tomatoes and simmer for 4 minutes.
In a bowl, whisk the coconut milk, mustard, harissa and miso. Add to the skillet with the shiitake, raisins, capers and stock. Simmer over low heat, stirring, until thickened, about 4 minutes. Season with salt and pepper.