Combine 2 tsp. genmaicha leaves and 1 1/2 cups boiling water; let steep 5 minutes, then strain into a bowl.
Meanwhile, heat 2 tbsp. oil in a large frying pan over medium heat. Add mushrooms and ginger; sprinkle with 1/2 tsp. salt and cook until mushrooms begin to shrink. Add brewed tea; cook 5 minutes. Stir in cabbage and cook until slightly wilted but still green and most of liquid has evaporated, about 5 minutes. Set aside, covered.
Slice tofu in half horizontally and set on paper towels. Cut an X through each half, forming 4 triangles per half, or 8 total. Blot tops with paper towels.
Pulverize polenta and peppercorns in a spice grinder. Add remaining 1 tbsp. tea and 1 tsp. salt and pulse just to combine.
Brush tofu on both sides with some oil. Liberally sprinkle oiled sides with polenta mixture and press on with your fingers.
Heat remaining 2 tbsp. oil in a large nonstick frying pan over medium-high heat. Cook tofu until deeply golden brown on one side, about 8 minutes. Flip and brown other side lightly, about 3 minutes more.
Arrange 2 tofu triangles on each of 4 warmed dinner plates. Reheat mushrooms and cabbage in pan, stir in green onions, and spoon mixture around tofu.