In a mixing bowl, mix together the garlic, ginger, turmeric, 1 teaspoon salt, 1/2 teaspoon pepper and the olive oil. Add the shrimp and mix to coat well.
Heat the oil in a large skillet over medium-high until shimmering. Add the shrimp in an even layer and cook,undisturbed, for 2 minutes. Pour in the coconut milk and soy sauce, stir to combine and turn the shrimp. Raise the heat to high and adjust it to maintain a simmer (avoid bringing to a boil), and cook until the liquid is slightly thickened and shrimp are almost cooked through, stirring occasionally. Stir in the kale in batches until wilted.
Remove from the heat and squeeze in the juice from a lime half. Adjust seasoning with more lime and salt as needed. Top with the chiles, scallions and cilantro, and serve with rice, noodles or naan.