Set your widest skillet over medium heat and when hot, swirl in 2 tablespoons of the oil, followed by the onions and cayenne. Fry until soft and they begin to color deeply, 10 to 12 minutes. Add the sesame oil, followed by the sweet potato, cabbage, and salt. Cover and cook until tender, stirring periodically, about 10 minutes. Allow to cool slightly.
In a mixing bowl, whisk together the egg, tahini, and lemon juice until combined. Add the potato-cabbage mixture, then fold in the panko or breadcrumbs. Add additional panko if the mixture seems loose, but err on the side of wet because the burgers will firm up as they cook and cool. If you have time, let the mixture sit for 20 to 30 minutes, and even overnight in an airtight container, then shape into 4 large or 6 smaller patties.
To cook, wipe out the skillet and return it to medium heat, then swirl in the remaining 2 tablespoons oil. Add as many burgers as will fit comfortably without crowding the pan (usually 2 or 3 for me), and cook until seared and crisped on the bottoms, 5 to 7 minutes, then flip and repeat on the other side, lowering the heat if they begin to burn. The burgers will firm up a bit as they cook, and further once they’re removed from the heat and have cooled slightly. Serve warm.
