Heat a large skillet. Add one-third of the baby spinach and cook over moderately high heat, stirring, until wilted. Transfer the spinach to a colander. Repeat with the remaining spinach in 2 batches. Press all of the excess water out of the spinach and coarsely chop it.
Heat the vegetable oil in the same skillet. Add the minced garlic and chiles and cook over moderate heat until fragrant, 2 minutes. Add the ground coriander and turmeric and cook, stirring, until fragrant, 1 minute. Add the chopped spinach and yogurt and cook over low heat, stirring, until the yogurt just begins to separate, 3 minutes. Season with salt and serve.
Make Ahead: The cooked spinach can be covered and refrigerated overnight. Reheat gently before serving.