In a large bowl, mix soy sauce, brown sugar, fish sauce, vegetable oil, lime juice, garlic, ground coriander, ground cumin, turmeric, and black pepper.
Add sliced beef to the marinade and toss to coat evenly. Cover and refrigerate for at least 1 hour, preferably 2 to 4 hours.
To make the peanut sauce, combine peanut butter, coconut milk, soy sauce, brown sugar, lime juice, red curry paste, ginger, and garlic in a saucepan over low heat.
Simmer gently for 3 to 5 minutes, stirring until the sauce is smooth. Add warm water gradually to reach desired dipping consistency. Remove from heat and set aside.
Thread marinated beef slices onto soaked wooden skewers, folding slices slightly for even cooking.
Preheat grill or grill pan to medium-high heat. Grill skewers for 2 to 3 minutes per side until cooked through and lightly charred. Alternatively, pan-sear in hot skillet with oil until browned on all sides.
Serve beef satay warm on a platter with Thai peanut sauce on the side. Garnish with chopped peanuts, fresh cilantro, lime wedges, and cucumber slices if desired.