Trim any excess fat from the chicken thighs and cut into 1/2- to 3/4-inch strips, about 1/2–3/4 inch thick and 3–4 inches long so they can be threaded on skewers.

Make marinade

In a medium bowl whisk together coconut milk, brown sugar, soy sauce, fish sauce, lime juice, minced garlic, grated ginger, turmeric, ground coriander, vegetable oil, salt, and black pepper until sugar dissolves and mixture is homogeneous.

Marinate

Place the chicken strips in the marinade, pressing them down so they are fully coated. Cover and refrigerate at least 30 minutes, preferably 2–4 hours (up to overnight) for best flavor.

Soak skewers

While the chicken marinates, submerge bamboo skewers in water for at least 30 minutes to prevent burning on the grill.

Assemble skewers

Preheat a grill or grill pan to medium-high. Thread 2–3 strips of chicken onto each skewer snugly but not overcrowded, leaving a small gap between pieces for even cooking. Reserve excess marinade.

Grill

Oil the grill grates or brush skewers with a little oil. Grill skewers over medium-high heat 3–4 minutes per side (about 8–10 minutes total), turning once or twice, until exterior is lightly charred and internal temperature reaches 165°F (74°C). During the last minute, brush lightly with reserved marinade and move to indirect heat to avoid flare-ups.

Rest

Transfer skewers to a plate and let rest 3–5 minutes before serving to allow juices to redistribute.

Peanut Sauce

Make the sauce: In a small saucepan over low heat combine the peanut butter, coconut milk (or water), soy sauce, brown sugar, lime juice, fish sauce, minced garlic, and red curry paste. Whisk continuously until smooth and warmed through, about 3–5 minutes. If the sauce is too thick, add water or additional coconut milk 1 tablespoon at a time until you reach a dipping consistency.

Season: Taste and adjust seasoning with salt, more lime for brightness, or a touch more sugar for sweetness. Remove from heat and transfer to a bowl. Sprinkle chopped toasted peanuts on top for texture.

To Serve

Arrange the grilled chicken satay on a platter with the peanut sauce in a small bowl. Garnish with chopped cilantro, cucumber rounds or pickled cucumber on the side, and lime wedges. Serve immediately.