Trim excess fat from the chicken thighs or beef. Slice across the grain into thin strips about 1/4–1/2 inch thick and 3 inches long so they thread easily on skewers.

Make marinade

In a large bowl combine light soy sauce, dark soy sauce, 3 tablespoons coconut milk, 1 tablespoon brown sugar, ground coriander, ground cumin, turmeric, minced garlic, minced shallot, chopped lemongrass, vegetable oil, kosher salt and black pepper. Whisk until sugar dissolves and mixture is uniform.

Marinate

Add the sliced meat to the marinade and toss to coat thoroughly. Cover and refrigerate for at least 1 hour, preferably 3–4 hours. For best flavor, marinate up to overnight (do not exceed 24 hours for chicken; up to 12 hours for thin-sliced beef).

Skewer meat

If using bamboo skewers, ensure they have soaked for 30 minutes. Thread 3–4 strips of meat onto each skewer, pressing gently so the strips lay flat and are evenly distributed. Leave a little space between pieces for even cooking. Place skewers on a tray and bring to room temperature for 15–20 minutes before cooking.

Preheat grill or broiler

Preheat a grill or grill pan to medium-high (about 400°F / 200°C). If using an oven broiler, set the broiler to high and position the rack about 6 inches from the heat source. Lightly oil the grill grates or brush the pan with a little oil to prevent sticking.

Cook satay

Grill skewers for 2–3 minutes per side, turning once or twice, until nicely charred at the edges and cooked through (internal temp 165°F / 74°C for chicken, 130–140°F / 54–60°C for medium beef). Brush occasionally with leftover marinade during the first half of cooking, but discard any marinade that has contacted raw meat. Total cook time 6–8 minutes depending on thickness.

Rest skewers

Remove skewers from heat and let rest on a plate for 3–5 minutes to allow juices to redistribute before serving.

Peanut Sauce

Make sauce

While the satay marinates or cooks, combine peanut butter, 1/2 cup coconut milk, soy sauce, 1 tablespoon brown sugar, lime juice, minced garlic, and red curry paste (if using) in a small saucepan over low heat. Stir constantly until the mixture becomes smooth and slightly glossy, 2–3 minutes.

Adjust consistency

If the sauce is too thick, add water 1 tablespoon at a time (about 2 tablespoons total) until you reach a pourable dipping consistency. Stir in fish sauce if using and taste; adjust with a pinch more salt, lime juice, or brown sugar as needed.

Finish and garnish

Transfer sauce to a serving bowl and sprinkle chopped roasted peanuts and chopped cilantro or sliced scallions on top.

Serve

Arrange the rested skewers on a platter with cucumber slices and steamed jasmine rice or rice cakes. Serve the warm peanut sauce on the side with lime wedges. Encourage diners to squeeze lime over the satay and dip into the peanut sauce.