Rehydrate the sea greens by pouring boiling water over the arame in a small bowl.
Let it soak for 1-2 minutes, then drain thoroughly.
In a food processor, pulse the trimmed scallions until minced and transfer to a large mixing bowl.
Add half of the tofu and the drained arame to the processor and pulse a few times until just crumbled.
Add this mixture to the bowl.
Place the remaining tofu in the food processor and blend until completely smooth.
Add the smooth tofu to the mixing bowl along with the panko, sesame seeds, soy sauce, and sesame oil.
Season generously with salt and pepper and mix until well combined.
Shape the mixture into 4 to 6 equal-sized patties. For the best results, let them rest for 10-15 minutes to firm up.
Heat the peanut oil in a large nonstick or cast-iron skillet over medium heat. Carefully place the patties in the hot pan and cook for about 5 minutes, until golden brown and they release easily from the pan.
Flip the burgers carefully and cook for another 3-4 minutes on the other side until heated through and golden.
Serve immediately on buns or with your favorite sides.