Heat the oil in a large skillet over medium heat. Add the shallot, garlic, ginger, and red pepper flakes and cook, stirring, until tender, about 2 minutes.
Add the ground chicken, salt, pepper, and white parts of the green onions. Cook, breaking up the meat with the edge of a spoon until cooked through, 5 to 7 minutes.
Add in the sesame oil, miso paste, sriracha, and coconut aminos and stir until well combined and the miso paste is well incorporated into the mixture.
Stir in the mint, cilantro, and green parts of the onion.
To serve, divide the lettuce in the bottom of a bowl. Spoon the miso chicken mixture over the top. Garnish with a little more mint and cilantro, a sprinkle of the peanuts for a crunch, and serve with a wedge of lime.