Blend shallots, garlic, lemongrass, and ginger with 2 tablespoons water until smooth. Transfer to a small bowl. Add fish curry powder and chili powder to form a paste.
Heat vegetable oil in a medium deep pan. Fry salted fish for 3 minutes on each side until lightly brown. Remove and set aside, leaving the oil in the pan.
Add spice paste and stir fry for 3 minutes. Add jalapeno peppers. Continue to stir fry for another minute.
Pour in coconut milk, cover, and bring to a boil.
Remove lid. Return fried salted fish to the pan. Cover and allow curry to simmer for 5 minutes.
Remove lid, add eggplants and green beans. Cover and bring it back to a boil. Remove lid, stir, and do a taste test. Add salt if necessary. Cover and simmer for 10 minutes or until eggplants and green beans are tender. Turn off stove.
Serve warm with steamed rice.