Set a large skillet or wok over medium-high heat and add the sesame oil. Once it's shimmering — this takes about a minute — add the grated ginger and minced garlic. Stir them around for about 30 seconds, just until the kitchen smells incredible and the ginger starts to sizzle. You want the aromatics fragrant but not brown. Burnt garlic is bitter garlic, and burnt ginger tastes acrid. Keep things moving in the pan.
Add the ground chicken to the skillet, breaking it up with a wooden spoon or spatula as it cooks. Here's where most people go wrong with ground chicken: they stir it too much too soon and it steams instead of browning. What you want to do is let the chicken sit in contact with the hot pan for about two minutes before you start breaking it up. Let it develop some color on the bottom. That golden-brown crust is where all the savory flavor lives — it's the Maillard reaction doing its thing, and it makes the difference between bland ground chicken and something that tastes deeply satisfying.
Once the chicken is golden and cooked through, pour in the coconut aminos and rice vinegar. If you want heat, add the sriracha now too. Stir everything together and let it cook for another 2 minutes. The sauce will reduce slightly and coat the chicken in this glossy, savory-sweet glaze. The coconut aminos bring that umami depth you'd get from soy sauce but with a slightly sweeter, more complex flavor and no soy if that's a concern for you.
Arrange the butter lettuce leaves on a platter — I like to cup them slightly so they're ready to be filled. Spoon the warm chicken filling into each leaf. Top with shredded red cabbage, a scatter of sliced scallions, a sprinkle of sesame seeds, and a squeeze of fresh lime juice. Add cilantro if you're in that camp.