Turn on the broiler, adjust the rack to the top third of the oven, and let it heat up. (It will take at least 20 minutes to warm up.)
In a medium-size shallow bowl, add enough soy sauce to cover the bottom. Add a drizzle of vegetable oil, salt, and pepper, and stir to combine.
Cut the block of tofu into 1-inch-by-2-inch rectangles. Peel the carrots, and cut them in half lengthwise, then in half again widthwise.
Cover a baking sheet with foil. Coat the carrots and tofu pieces in the soy sauce mixture using your fingers, then lay the pieces on the baking sheet. Save the sauce.
Put the baking sheet under the broiler and set the timer to five minutes.
Take out the sheet, turn the tofu pieces a quarter turn, and put the sheet back in for another five minutes. Take it out, turn the tofu another quarter turn, flip the carrots over, and put the sheet back in for an additional five minutes. Remove the sheet from the oven. The carrots will be blackened and the tofu browned.
If you’re using a green onion, slice it, including the white part. Add it to the soy sauce mixture along with a few drizzles of toasted sesame oil and a few generous shakes of rice vinegar. Season with salt and pepper.
Add the carrots and tofu to the sauce, and toss to coat. Eat as is, or with rice.