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.
Add in the fresh ginger and garlic and saute until fragrant, about one more minute.
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.
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.
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.