Add the rice and oil to a skillet over medium heat and toast, shaking frequently, until browned, about 3 minutes. Transfer to a plate and let cool completely.
Grind the cooled rice to crumbs in a mortar and pestle or spice grinder.
In the same skillet, cook the garlic in the oil over medium-low heat, stirring occasionally, until golden brown, about 1 minute.
Add 1 teaspoon of sugar and cook for 20 seconds.
Add the ground turkey to the skillet. Break it up into small pieces and cook over medium-high heat until no pink remains, about 3–5 minutes.
Add 2 shallots, ground dried chilies, 1 teaspoon fish sauce, salt, and pepper to the turkey mixture.
Raise the heat to high and cook, stirring constantly, for about 6 minutes, until turkey cooks fully and becomes golden brown. Transfer to a bowl and set aside.
Make the dipping sauce: In a small bowl, whisk together the lime juice, fish sauce, sugar, and sliced Thai chili.
Serve the lettuce leaves, turkey mixture, rice powder, sliced chili, torn herbs, sliced Lebanese cucumber, shallot slices, and dipping sauce on a plate. Let each person spoon the turkey mixture into lettuce leaf cups before adding a sprinkle of rice powder and other toppings. Dip in the sauce and eat.