Shrimp, okra, and kabocha-squash stew shows the African influences in northern Brazilian cuisine.
Toss shrimp, ginger, and paprika in a large bowl; season with salt and pepper.
Heat 3 tablespoons oil in a large saute pan over medium-high heat until hot but not smoking. Working in batches, and adding more oil as needed, cook shrimp, turning once, until browned on both sides, about 4 minutes total. With a slotted spoon, transfer to a plate to cool; keep pan on stove with heat turned off.
Set aside 6 shrimp for garnish. Shell remaining shrimp, transferring shells and heads to a large square of cheesecloth as you work. Set aside shrimp; tie cheesecloth securely into a bundle.
Add remaining tablespoon oil to pan, along with shallots, garlic, chile, and cumin. Cook, stirring, over medium heat for 1 minute. Stir in squash; add cheesecloth bundle and 1 cup water. Reduce heat to medium-low. Cover; simmer until squash begins to soften, about 15 minutes.
Stir in coconut milk and okra. Simmer, covered, until squash is cooked through and soft and the sauce is thick, about 30 minutes. Transfer cheesecloth bundle to a sieve set over the pan; squeeze liquid into sauce, and discard bundle. Stir in reserved shelled shrimp and cilantro. Season with salt and pepper.
Divide among small serving bowls. Garnish with reserved shell-on shrimp, and, if desired, cilantro leaves.
If you can't find whole shrimp (with heads intact), use regular medium unpeeled shrimp.