Place 12 bamboo skewers in a shallow dish or baking tray and cover them fully with cold water. Allow the skewers to soak for 30 minutes at room temperature. Soaking saturates the bamboo with water, which prevents the exposed ends from catching fire during grilling.
Place the boneless, skinless chicken thighs on a cutting board and trim away any large pieces of visible fat. Slice each thigh lengthwise into strips approximately 2.5cm / 1in wide and 10cm / 4in long. Consistent strip dimensions ensure each piece marinates evenly and cooks to the same internal temperature across all 12 skewers.
Combine the tamari, coconut milk, fish sauce, brown sugar, ground turmeric, ground coriander, ground cumin, white pepper, and minced garlic in a medium mixing bowl. Whisk the mixture for 60 seconds until the sugar dissolves and the turmeric disperses uniformly throughout the liquid. The marinade should appear a consistent golden-orange color with no visible clumps of spice.
Add the sliced chicken strips to the bowl with the marinade and toss thoroughly using tongs or clean hands until every surface of every strip is coated. Cover the bowl with plastic wrap and refrigerate for 2 hours. A minimum of 2 hours allows the turmeric, cumin, and coriander to penetrate the surface layer of the chicken and bind flavor into the meat.
Remove the marinated chicken from the refrigerator and thread one strip lengthwise onto each soaked bamboo skewer, weaving the skewer through the center of the strip in three points so the meat lies flat rather than bunching. Arrange the loaded skewers on a wire rack set over a baking sheet. Return them to the refrigerator uncovered for 30 minutes. The dry-rest period draws surface moisture away from the chicken, which produces deeper grill marks and a drier exterior char during cooking.
Preheat an outdoor grill or stovetop grill pan over high heat for 5 minutes until the surface reaches approximately 230°C / 445°F. Brush the grill grates with 1 tablespoon of neutral oil using a folded paper towel held with tongs. The grill is ready when the oil immediately shimmers and produces light wisps of smoke on contact with the grates.
Place the skewers on the oiled grill grates, leaving at least 2.5cm / 1in of space between each skewer. Grill the chicken for 4 minutes on the first side without moving them, until distinct char marks appear and the strips lift cleanly from the grates. Flip each skewer using tongs and grill for 4 minutes on the second side until the chicken is cooked through, shows char marks on both sides, and an instant-read thermometer inserted into the thickest part of the strip reads 74°C / 165°F.
Transfer the finished skewers to a clean serving plate and allow them to rest for 3 minutes before serving. Resting allows the internal juices to redistribute throughout the meat, which keeps each strip moist when bitten. Serve the Chicken Satay alongside peanut sauce and fresh cucumber slices.