Heat the sesame oil in a medium skillet over medium-high heat. Add the diced onion, grated carrot, minced chili, and chopped mushrooms and cook, stirring occasionally, until the mushrooms have released their liquid and the onions are beginning to become translucent.
Add the minced garlic and grated ginger. Cook, stirring, for 30 seconds until fragrant. Add the tamari and salt, stir to combine, then remove from the heat and allow to cool.
Spoon the cooked vegetable mixture into the lettuce leaves, and top with raw purple cabbage to add back a bit of crunch. Finish with green onion, sesame seeds, a squeeze of lime, and red chili flakes (if you prefer additional heat)! Best served cold.