In a small bowl, combine the minced garlic, finely grated ginger, and lime zest, then whisk in the fish sauce, tamari, honey, lime juice, and chili. Add the turmeric and stir well to create a smooth, cohesive marinade. I like to let the aromatics sit in the acidic lime juice for a minute before mixing everything together—it helps mellow out the raw garlic bite and lets the flavors meld slightly before they hit the chicken.
Pat the chicken drumsticks dry with paper towels—this helps the marinade adhere better rather than sliding off wet skin. Place the drumsticks in a large bowl or on a sheet tray and generously coat each piece with the marinade from Step 1, making sure to work it under the skin and into any crevices. Let them sit at room temperature for at least 15 minutes while you preheat the oven; this gives the flavors time to start penetrating the meat.
Preheat your oven to 190°C (375°F). While it heats, drizzle the coconut oil and 1 tablespoon of the olive oil onto a large baking tray or rimmed sheet pan, tilting to coat evenly. This dual-oil approach gives you the high smoke point of olive oil combined with the subtle flavor of coconut oil. I find this combination prevents sticking while adding depth to the chicken's exterior.
Transfer the marinated drumsticks to the oiled baking tray, arranging them skin-side up in a single layer without crowding. Roast for 15 minutes, then remove the tray from the oven and brush each drumstick generously with the remaining marinade pooled at the bottom of the bowl. Return to the oven and continue roasting for another 10-15 minutes until the skin is caramelized and the internal temperature reaches 165°F (74°C) when measured at the thickest part of the thigh. The staggered brushing halfway through ensures a rich, glossy finish while keeping the meat moist.
Once the drumsticks are fully cooked and golden, remove them from the oven and immediately drizzle with the sesame oil and coconut milk, followed by the remaining 1 tablespoon of olive oil. This creates a rich, silky glaze that pools around the chicken. Scatter the fresh cilantro over the top just before serving for brightness and a fresh Thai finish. Season with the salt to taste.