Mix together soy sauce, syrup, oil and toss with mushroom. Set 5-10 minutes, stirring now and then.
Heat the olive oil in large skillet, add the mushrooms and any juices, and cook until crispy and golden. Scoop out the mushrooms and set aside.
Cook the pasta, reserving ¼ cup of the cooking water.
Put the pan with the mushroom juices back on a medium heat and add the vegan butter. Saute onion until soft. Add garlic and radicchio, and cook a few minute to wilt the radiccio.
Add the pasta, pasta water and balsamic, stirrying to coast.
Turn off heat, stir through the mushrooms and olives, season and serve topped with vegan parmesan if desired.