Combine first 4 ingredients, 1/4 cup peanuts, and 3 tablespoons oil in a small bowl; stir with a whisk.
Cut each tofu block crosswise into 8 (1/2-inch-thick) slices. Arrange tofu on several layers of paper towels. Top with several more layers of paper towels; top with a cast-iron skillet or other heavy pan. Let stand 30 minutes. Remove tofu from paper towels.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add 8 tofu slices to pan; sauté 4 minutes on each side or until crisp and golden. Remove from pan, and drain tofu on paper towels. Repeat procedure with remaining 1 tablespoon oil and remaining 8 tofu slices. Place 1 cup greens on each of 8 plates. Top each serving with 2 tofu slices, 3 tablespoons miso mixture, and 1 1/2 teaspoons chopped peanuts. Garnish each serving with chives, if desired.