To make the crispy salt and pepper tofu
To press and drain the tofu, remove from the package, discard the water, and place on a dinner plate. Set a smaller plate on top, and then weigh down with a heavy object (such as a can of beans or a jar of jam) to press and release the water. Let sit for about 15 minutes. Drain the residual water.
Lay the tofu flat on a cutting board. Halve on the diagonal so that you have two right-angle triangles. Lay each triangle on its longest side so that the right angle is at the top, like a mountain peak. Cut lengthwise into four identical triangles about ½ inch thick. (You will end up with eight of these). Now lay each triangle down flat and cut crosswise into three smaller triangles (they will not be identical), for a grand total of twenty-four pieces. Arrange the tofu on a tray or large plate.
In a small bowl, whisk the oil, salt, and pepper with a fork until the salt is nearly dissolved. Generously brush the tofu on both sides with the seasoned oil.
Heat a 10- to 12-inch skillet (cast-iron works great here) over medium-high heat until nearly smoking hot. Cook the tofu in batches for 3 to 5 minutes on each side, or until golden brown and crispy, adjusting the heat as needed to prevent burning. The tofu is best eaten the day it is made, though it will keep for 1 to 2 days in the refrigerator; reheat in a dry skillet.
To make the caprese salad
First, make the basil oil. Bring 4 cups water to a boil over high heat in a medium pot and add the basil. Boil for about 30 seconds, drain, and immediately transfer to a bowl of ice water. Using your hands, squeeze the basil firmly to extract as much water as possible.
Combine the basil and oil in a stand blender or mini-chopper and blend until fairly smooth. Pour the oil over a strainer into a glass jar, gently pressing on the basil to extract as much oil as possible. This may take up to 20 minutes. Set aside until ready to use.
Arrange the tomatoes on a platter or large plate and generously spoon the basil oil over the top. (You probably won’t need all of the oil.) Arrange the tofu over the top, estimating about 4 triangles per serving. Decorate the perimeter of each plate with cherry tomatoes. Scatter the basil leaves on top and serve.
Kitchen notes: Both the basil oil and the tofu can be made in advance. Store any leftover oil in the refrigerator and use in vinaigrettes or to lather a bowl of pasta or your favorite grain. Reheat the tofu in a dry skillet. Look for extra-firm or firm tofu packed in water in the refrigerated section of the supermarket.