1. Combine 2 tsp. genmaicha leaves and 1 1/2 cups boiling water; let steep 5 minutes, then strain into a bowl.
2. 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.
3. 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.
4. Pulverize polenta and peppercorns in a spice grinder. Add remaining 1 tbsp. tea and 1 tsp. salt and pulse just to combine.
5. Brush tofu on both sides with some oil. Liberally sprinkle oiled sides with polenta mixture and press on with your fingers.
6. 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.
7. 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.