In a small pan, combine half the garlic with the hoisin sauce. Cook over medium heat until thickened and beginning to turn syrupy, 2-5 minutes depending on the pot used. Stir often to prevent burning.
In a large skillet, heat half the oil over medium-high heat until shimmering. Add the onion, ginger, and remaining garlic and sauté, stirring occasionally, until golden and soft. Add pork and break up with a wooden spoon. Cook, stirring occasionally, until all the moisture has evaporated and the pork is cooked through and tender.
In a second skillet, heat the remaining oil over medium-high heat until shimmering. Add the carrot and potato. Cook until almost tender, then add red bell pepper and water chestnuts and cook for a few minutes longer. Add this mixture to the pork along with the reduced hoisin sauce. Stir well to coat the pork and season to taste with salt and pepper.
Separate and wash lettuce leaves; serve alongside pork.