1. Heat 1 tablespoon oil in a large skillet over medium-high heat. Add garlic and 2 teaspoons chili paste. Cook, stirring constantly, until garlic is softened, about 1 minute. Add pork and cook, breaking up with a spoon, until pork is cooked through, 6-8 minutes. Transfer pork mixture to a plate and let cool.
2. Meanwhile, whisk lime zest, lime juice, fish sauce, brown sugar, remaining 2 tablespoons oil, and remaining 2 teaspoons chili paste in a small bowl to combine.
3. Combine chopped onion, chopped mint, and half of dressing in a medium bowl. Add pork mixture and toss to combine. Toss lettuce, cucumber, sliced onion, whole mint leaves, and remaining dressing in a large bowl. Arrange salad and pork on a platter.
4. Pork mixture can be made 1 day ahead. Cover and chill. Serve cold or room temperature.
Recipe adapted from: https://www.bonappetit.com/recipe/spicy-pork-salad