Preheat the oven to 350° F. Grate the zucchini to create large strands, using the large holes of a box grater. Toss with salt and then leave in a strainer for 15 minutes. Using your hands or by wrapping the zucchini in cheesecloth, squeeze out any excess liquid.
Combine the zucchini with the almonds, basil, flour, egg, and black pepper. Add the bread crumbs, adding more if the mixture hasn't become pliable. (It will be a very wet mixture, though.) Shape into 4 patties.
Heat the oil in an oven-safe sauté pan over a medium flame. Cook the burgers, 2 to 4 minutes per side, until golden brown. Transfer the pan to the oven and cook for 12 to 15 minutes more, until firm.