Make ginger juice with the 3 inch knob of fresh ginger by grating it into a thin cotton kitchen towel or piece of cheesecloth, then squeeze the juice into a bowl (you want 2 tablespoons); set aside.
In a medium saucepan, bring the wine to a boil and cook for about 2 minutes; add vegetable stock, ginger juice, mushrooms, and ginger matchsticks.
Cook for 3 minutes, then strain the broth back into the saucepan, reserving both the broth and the solids; set aside.
Blend the butter into the broth with an immersion blender; return reserved solids to broth, along with 2 tablespoons lime juice (any extra can be saved for another use), scallions, cilantro, cayenne, and lime zest; cook for 2 minutes then remove from heat.
Preheat a grill to medium high; season bass pieces with salt and pepper, drizzle with olive oil.
Place bass skin side down on grill and cook 2 minutes, rotate a 1/4 turn and cook 3 minutes; flip and cook until flesh is easily flaked with a knife, about 3 to 5 minutes.
Remove fish to a large oval platter, reheat broth and vegetables, then pour it around the fish; garnish with fresh cilantro sprigs.