1/2 cup (4 ounces) tamarind pulp with seeds (see Note)
1 tablespoon vegetable oil
1 pound medium shrimp, shelled and deveined, shells reserved
2 small red onions—1 coarsely chopped, 1 minced
1 tablespoon tomato paste
1 1/2 cups cubed fresh pineapple (1/2-inch cubes)
1/2 jalapeño chile, seeded and minced
Freshly ground pepper
In a small saucepan, bring 2 cups of the water to a boil. Remove from the heat and add the tamarind pulp. Cover and let stand until softened, about 30 minutes. Pass the tamarind mixture through a coarse strainer; discard the seeds.
Meanwhile, in a large saucepan, heat the oil. Add the shrimp shells and cook over high heat, stirring, until pink, about 3 minutes. Add the coarsely chopped onion and cook over moderately high heat, stirring, until softened and starting to brown, about 3 minutes. Add the tomato paste and cook, stirring, until it starts to caramelize, about 2 minutes. Add the remaining 8 cups of water and bring to a simmer, scraping up the browned bits on the bottom of the pan. Simmer over low heat for 30 minutes. Strain the broth and return it to the saucepan.
Add the minced onion and the pineapple to the broth. Cover and simmer over low heat for 10 minutes. Stir in the tamarind puree and return to a simmer. Add the shrimp and cook over moderately high heat until opaque throughout, about 3 minutes. Add the jalapeño and season with salt and pepper. Serve hot.
The recipe can be prepared through Step 2 up to 2 days ahead. Refrigerate the broth and tamarind puree separately.
Tamarind pulp is available at Asian, Latin and Caribbean markets.