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Heat the oil in a Dutch oven or large deep skillet over medium-high heat, and saute the onion, carrots, and celery until they start to soften, about 5 minutes.
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Add in the fresh ginger and garlic and saute until fragrant, about one more minute.
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Add in the tamari, maple syrup, split peas, and water and bring the mixture to a boil. Lower the heat to a simmer, so that the mixture is still gently bubbling, and cover with a lid to simmer until the liquid is absorbed and the split peas are tender.
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Remove the lid and stir well to allow any remaining liquid absorb or evaporate. The filling should not be watery. Allow the filling to cool for at least 5 minutes before spooning it into butter lettuce leaves. Use 2 leaves per wrap to make sturdier.
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Garnish each wrap with shredded carrots, fresh cilantro, and a squeeze of fresh lime juice, if desired, and serve right away. Leftover filling can be stored in an airtight container for up to a week. Store the lettuce leaves separately to help prevent them from wilting.