Make the Basil Pistachio Pesto (see next recipe card). You can do this a few days in advance.
Slice & press the tofu: Slice the tofu crosswise into ½” (12 mm) slabs. Cover with a thin dish towel (or a few paper towels); set a heavy book on top to press for 10 minutes to release some excess water.
Meanwhile, make the Quick & Spicy Slaw. In a medium bowl, combine the cabbage, carrot, and jalapeño.In a small bowl, whisk together the lemon juice, vinegar, mustard, ½ tsp maple syrup, ¼ tsp kosher salt, and pepper to taste. Stream in the olive oil until emulsified. Taste, adding more olive oil for richness, more maple syrup for sweetness, or salt to taste.Pour dressing over veggies and toss to coat. Season to taste with salt and pepper or more olive oil or lemon juice as desired. Make the tofu batter: In a small bowl, combine the cornstarch, onion and garlic powder, 1 ¼ teaspoons kosher salt, and several cracks of black pepper. Whisk well to combine.
Batter the tofu: Add the tofu slabs to a gallon-size ziploc bag. Pour the cornstarch seasoning on top. Seal the bag, and gently flip the bag back and forth and side to side several times until the tofu is well-coated, shimmying the bag as needed. Be gentle, taking care to not break the tofu (see Note 1).
Grab a wire rack and fit it over a sheet pan or place a towel underneath it.
Cook the tofu: Heat a large frying pan over medium-low heat for 2 minutes, then add the avocado oil and heat for 1 minute, or until shimmering. Increase the heat to medium if using nonstick, or just below medium if using carbon steel or cast iron. Carefully add half of the tofu (the tofu won’t sear evenly if you cook it all in one batch).Fry the tofu for 5 to 6 minutes until crispy and nicely golden brown on the bottom, rotating the pan occasionally for even heating and so the oil gets evenly spread out.Flip the tofu and cook for 3 to 5 minutes on the second side, or until golden brown and crisp on the other side (lower the heat if it starts to char). Transfer tofu to the wire rack.To prevent charring, before cooking the second batch of tofu, add another drizzle of oil to the pan and reduce the heat a touch. The second batch may cook slightly quicker. Sandwich Toppings: Slice the tomatoes and avocado. Sprinkle them with salt and pepper to season.
Toast the rolls/buns. If desired, spread some butter onto each slice of bread; toast buttered-side down in the frying pan over medium or medium-low heat until golden brown. Or, toast in a toaster oven.
Assemble: Spread about 1 tablespoon Basil Pesto across the surface of each slice of toasted bread. Add a lettuce leaf. Layer with crispy tofu, seasoned tomatoes and avocado, and some Quick Slaw. Top each with a basil leaf or two.