To begin, first press excess moisture out of the tofu: prepare a plate with a lint-free cotton tea towel or some paper towels. Remove the tofu from its package and place it on the towel. Put another paper towel on top, then a pie or cake pan, then set a couple of things in the pan to gently press on the tofu—I used a regular sized jar of peanut butter. Let it just sit for half an hour or so.
Put together the sauce ingredients in a small bowl. That will take you less than a minute and then you can just go have a nice sit-down for 30 or 40 minutes.
Next, cut the tofu into cubes, and put the cubes in another small bowl. Add the 3 tablespoons of cornstarch and gently toss everything with your hands until the tofu is evenly coated. Add more cornstarch if it looks like you're not getting adequate coverage. Set the bowl aside.
Heat 1 tablespoon of oil to medium in a wok or a big heavy-bottomed skillet, then add the tofu cubes and sauté them, top and bottom, until they are golden. Scoop them out of the pan into a clean bowl. Add the rest of the oil to the pan, then sauté the onion or shallot and the garlic for a minute. Add the green pepper chunks and sauté them for two or so minutes.
Reduce the heat to low, and return the tofu to the pan. Give the sauce ingredients a good stir, then pour the sauce into the hot pan and stir everything gently. The sauce will thicken right away—you may need to add more water if it is too thick. Scatter the black pepper over everything, then, at the last, add the fresh cucumber. Stir again, and that's it. Serve on plates or in shallow bowls and top with green onions, if using.