Cut a small square of cheesecloth and put the peppercorns, coriander seeds, mustard seeds, cloves, and bay leaf in the middle of the cloth. Gather the edges into a pouch and secure with twine.

Heat the oil in a 4-quart heavy-duty non-reactive saucepan over medium heat. Add the onion, garlic, and ginger and cook, stirring occasionally, until soft but not browned, 3 to 5 minutes. Reduce the heat to medium low and add the tomatoes, jalapeno, sugar, and the spice bundle. Cook, stirring frequently, until very thick and most of the liquid has evaporated, 25 to 30 minutes. Season to taste with salt and pepper, discard the spice bundle, and let cool.

Bring a medium pot of salted water to a boil over high heat. Prepare an ice bath by filling a medium bowl with several inches of ice water. Blanch the basil in the boiling water for 10 seconds. Drain and immediately plunge into the ice bath to cool. Drain again and gently squeeze out any water. Put the basil and the oil in a blender and process until pureed, about 2 minutes. Line a fine sieve with cheesecloth and strain the oil into a small bowl, using a spoon or small spatula to push the oil through the cheesecloth. Discard the cheesecloth and set the oil aside.

Pick over the crab to remove any cartilage or shells. Work with the crab gently, being careful not to break up the meat. Put the crab in a medium bowl and add the lime juice, basil, shallot, coconut milk, Espelette pepper (if using), a pinch of salt, and a few grinds of pepper. Gently toss to coat and let marinate for about 10 minutes at room temperature. Put the crab in a fine sieve over a medium bowl and drain for at least 5 minutes.

Put a 2-1/2-inch-diameter ring mold in the center of a small plate, spread about 2 tablespoons of the chutney in the bottom, and top with 1/2 cup of the crab mixture. Carefully remove the mold. Repeat to make 5 more servings. Drizzle some basil oil around each plate, and garnish the top of each "cake" with toasted coconut flakes and basil tops. Serve immediately.