Heat a large skillet over medium heat and add the ground pork. Cook until browned and no longer pink, breaking it into small pieces with a spoon as it cooks.
Add the minced garlic, diced shallot, and sliced chilies to the skillet. Stir and cook for 1 to 2 minutes until the mixture becomes fragrant.
Stir in the fish sauce, oyster sauce, and brown sugar. Continue cooking for 2 minutes to let the flavors combine.
Remove the skillet from the heat and fold in the Thai basil leaves until they wilt slightly from the residual heat.
Spoon the pork mixture into the butter lettuce leaves and serve with lime wedges on the side.