Remove the skin from the chicken breast and slice lengthwise into strips about 1/4 inch (0.5 cm) thick. In a mixing bowl, combine the chicken with turmeric, salt, sugar, coconut milk, and evaporated milk. Mix well and marinate in the refrigerator for at least 2 hours. Thread the marinated chicken onto skewers.

To make the peanut sauce, blend the galangal, lemongrass, paprika, and coconut milk together until smooth. Pour into a pan and cook until fragrant. Add the ground roasted peanuts, then season with salt, tamarind paste, and palm sugar. Simmer until thickened, then remove from heat. For a deeper color, add chili oil from chili paste if desired.

For the cucumber relish (Ajaad), combine vinegar, sugar, and salt in a saucepan. Heat until the sugar and salt dissolve completely, then remove from heat and let cool until slightly thickened. Slice the cucumber, red chili, and shallots or red onion, place in a bowl, and pour the cooled vinegar mixture over the vegetables.

Grill the chicken skewers over low heat, basting occasionally with the coconut milk and evaporated milk mixture. Grill until cooked through.

Arrange the chicken satay on a plate, garnish with cilantro leaves, and serve hot with the peanut sauce and cucumber relish.