Stir garlic, turmeric, chili powder, basil, and cayenne pepper together in a small saucepan; heat over medium heat until aromatic, about 1 minute. Melt butter into the mixture, add onion, and cook until the onion is softened and translucent, about 5 minutes. Scoop onion mixture from saucepan into a slow cooker, reserving as much butter in the saucepan as possible.
Increase heat under saucepan to medium-high heat. Saute frozen shrimp in hot butter until just firm, about 2 minutes; transfer mixture to slow cooker. Add ham, ham bone, black beans, and tomatoes to the slow cooker.
Cook on High until the ham on the bone is falling off, 4 to 6 hours (or on Low 6 to 8 hours).
Remove and discard ham bone, stir coconut milk into the mixture, continue cooking on Low until the coconut milk is warmed, about 30 minutes.
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