In a 4-quart pot, heat the oil over medium-high heat. Stir in the diced shallots and cook until softened, about 1 minute (this will take a few more minutes if using onion). Add the garlic and chiles, decrease the heat to low, and cook, stirring frequently, until the garlic has begun to turn golden but has not started to brown, 1 to 2 minutes. (If the garlic starts to stick to the bottom of the pot, turn off the heat for a minute and stir, letting the garlic cook off the heat to avoid scorching it.)

Stir in the turmeric, paprika, cayenne, and salt. Add the tomatoes and cook over medium-low heat, stirring occasionally, until the tomatoes lose their shape and form a sauce, about 10 minutes. Stir in the okra, sliced shallots, and fish sauce and cook for 2 to 3 minutes more or until the okra is just tender but not mushy. Season with more fish sauce or salt if desired.

Cut the eggs in half. Nestle the eggs, cut-side up, in the pot and bring to a simmer. Gently stir the curry, ensuring that the eggs hold their shape, until the eggs are heated through. Include 1 or 2 egg halves in each serving. Serve with a bowl of cilantro sprigs at the table. Generously add the cilantro for a final flavor burst.