Drain and rinse with cold water, then drain again.
Slice both varieties of mushrooms and saute over medium-high heat in 1 T. of butter and the olive oil. Sprinkle with salt and pepper and cook, stirring often, until mushrooms are lightly browned, about 3 to 4 minutes.
Add remaining tablesopon of butter to pan. When melted, add ginger and garlic and stir until fragrant, 1 minute. Then add radicchio and edamame and stil until radicchio is wilted, 1 to 2 minutes.
Remove from heat.
In a large bowl, whisk vinegar, mustard, and soy sauce until combined.
Add cooked pasta and mushroom mixture and stir gently to coat.
Add salt and pepper to taste. Can be served warm or let cool to room temperature. Top with shaved fresh parmesan cheese (not dried) just before serving.