Heat 2 tablespoons oil in a 5- to 6-quart heavy pot over medium heat until it shimmers. Cook onion, stirring occasionally, until tender, about 7 minutes. Add spinach, chile, 2 tablespoons water, and 3/4 teaspoon salt and cook, uncovered, stirring occasionally, until spinach is wilted, 3 to 5 minutes. Remove from heat and stir in yogurt.
Heat remaining 1 1/2 tablespoons oil in a small heavy skillet over medium-high heat until it shimmers, then cook mustard seeds until they begin to pop and/or turn gray, then add cumin seeds and red pepper flakes and cook, stirring, until cumin seeds brown, about 30 seconds more. Add curry leaves (if using), covering skillet immediately for a few seconds, then stir spice mixture into spinach mixture. Season with salt. Serve warm.
