Slice tofu lengthwise into 4 pieces. Lay the pieces onto several layers of paper towels and top with more paper towels. Let rest 5 minutes. Slice each piece diagonally into 2 triangles. Arrange the tofu in a shallow baking dish.
Whisk together the sherry, soy sauce, and sesame oil. Spoon mixture over tofu and chill for 20 minutes.
Preheat oven to 450 degrees F.
Bake tofu for 25 minutes. Take out of oven and let rest until room temperature then refrigerate for 30 minutes.
Mix together the greens, cucumbers, and green onions. Whisk together lemon juice, olive oil, vinegar, sugar, salt, pepper, and garlic. Pour mixture over top of greens and top with tofu.