Place the carrot and radish matchsticks in a large lidded glass jar or dish along with the rice vinegar, sugar, kosher salt, and one cup of very hot water. Seal and shake until the sugar has dissolved. Set aside to pickle.*
Combine the sauce ingredients along with one tablespoon of water in a medium bowl. Whisk until well-combined; set aside.
Cut the protruding stems off the collard leaves to form a (roughly) circular shape. Hold a sharp knife parallel to the bottom side of the leaf and slice off as much of the remaining tough stem as you can. Heat a large pan over medium heat. Add one tablespoon of water along with the prepared leaves. Cover and steam for 1 to 2 minutes, until bright green and pliable. Do not over-steam, or they will become fragile and tear. Set the steamed greens aside to cool.
Wipe the water out of the pan. Add one tablespoon of peanut or grapeseed oil and heat over medium-high. Once the oil is shimmering, add the sliced tofu and fry, turning occasionally, until browned (about 4 to 5 minutes).
Meanwhile, whisk the soy sauce, sesame oil, and brown sugar together in a small dish. Once the tofu has browned, pour the sauce into the pan and toss with the tofu. Continue to cook until the sauce thickens, coats, and caramelizes the tofu; about 2 to 3 minutes.
Build the wraps: lay one collard leaf face-down on a cutting board. Fill with roughly one-fifth of the tofu, pickled vegetables, cilantro, and mint (if using). Roll up the collard, tucking in the sides as you go, to form a burrito-like wrap. Slice down the middle, through the middle rib, to cut in half. Repeat with remaining ingredients. Serve with prepared dipping sauce.
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Notes
*This may be done several days in advance. You may also choose to keep the carrot and radish separate; do so by dividing the pickling mixture in half.To store Collard Green Wraps, place them in an airtight container and refrigerate for up to 3 days. Freezing is not recommended as it affects the texture.To reheat, use a microwave on low power for 1-2 minutes or warm them in a pan over medium heat for a few minutes until heated through. Ensure the wraps are covered while reheating to prevent drying out.