In a large bowl, whisk together soy sauce, brown sugar, fish sauce, vegetable oil, lime juice, garlic, coriander, cumin, turmeric, and black pepper.
Add beef slices to the marinade and toss until well coated. Cover and refrigerate for 1 to 4 hours.
In a saucepan over low heat, combine peanut butter, coconut milk, soy sauce, brown sugar, lime juice, red curry paste, ginger, and garlic, stirring until smooth.
Simmer the sauce gently for 3 to 5 minutes, then thin with warm water to desired consistency. Remove from heat and set aside.
Thread marinated beef slices onto soaked wooden skewers, folding slices for even cooking.
Preheat grill or grill pan to medium-high heat. Grill skewers 2 to 3 minutes per side until charred and cooked through.
Alternatively, pan-sear skewers in a hot skillet with a little oil, turning until browned on all sides.
Arrange cooked beef satay on a platter. Serve warm with Thai peanut sauce and garnish with chopped peanuts, cilantro, and lime wedges.