In a large saucepan, cover the crosnes with water and add a pinch of salt. Boil until the crosnes are tender, 10 minutes; drain. Slice the crosnes 1/4 inch thick.
Fill the large saucepan with water and bring to a boil. Add the kale and cook until just tender, about 3 minutes. Drain the kale and let cool slightly. Squeeze out any excess liquid from the kale leaves and then coarsely chop them.
In a small skillet, heat 2 tablespoons of the blended oil. Add the onion and a pinch of salt and cook over moderately low heat, stirring occasionally, until browned.
Add the potatoes and cook until tender and browned.
In a nonstick skillet, melt the butter in 2 tablespoons of the blended oil. Add the crosnes in an even layer and cook over high heat until browned on the bottom, about 3 minutes. Turn the crosnes, reduce the heat to moderately high and continue cooking until starting to brown, about 2 minutes. Push the crosnes to the side of the skillet.
Add 1 more tablespoon of the oil and the mushrooms. Season with salt and pepper and cook over moderately high heat until browned, 3 minutes. Add the remaining 1 tablespoon of oil along with the kale and onion and cook, stirring, until hot. Season with salt and pepper and serve.