Place tofu onto a plate and place another plate on top. Set a 3 to 5 pound weight on top. Press tofu for 20 to 30 minutes; drain and discard the accumulated liquid.
Cut tofu into 2x4-inch strips about 1/4-inch thick.
Heat 1 tablespoon oil in large skillet over medium-low heat. Cook tofu strips in the oil until golden brown, 2 to 3 minutes per side. Stack tofu strips horizontally in a dish with sloping sides, like a teacup saucer.
Heat remaining 1 tablespoon oil in the same skillet. Add green onions; cook and stir until fragrant, 10 to 20 seconds. Spoon green onions over tofu while they are still sizzling. Coat with soy sauce. Let sit until tofu soaks up flavors, 3 to 5 minutes.