Step 1

Place hot water and tamarind fruit in a bowl. While submerged in water, separate tamarind pulp from seeds with your fingers. Let mixture stand 10 minutes. Meanwhile, cut lemongrass stalks into 3-inch pieces. Working in 4 batches, place lemongrass pieces in a mortar; smash with pestle until fragrant and fibers are separated. Set aside.

Step 2

Pour soaked tamarind mixture through a fine wire-mesh strainer into a small bowl, rubbing and pressing softened tamarind pulp back and forth across strainer to extract liquid. Discard solids; reserve strained liquid.

Step 3

Heat vegetable oil in a large saucepan over high. Add shallots and smashed lemongrass; cook, stirring often, until shallots begin to brown, about 5 minutes. Stir in sambal oelek, ketchup, sugar, bouillon granules, salt, achiote oil, and strained tamarind liquid. Bring to a boil. Reduce heat to medium; simmer, stirring often, until flavors have melded and sauce thickens slightly, 5 to 8 minutes. Remove from heat. Pour through a fine wire-mesh strainer into a heatproof bowl, pressing on solids with a spoon to extract liquid. Discard solids. Cover to keep warm until ready to serve.

Step 4

Heat canola oil in a wok over medium-high to 350°F. Place 1/2 cup cornstarch in a shallow bowl. Whisk together flour, baking powder, and remaining 1/2 cup cornstarch in a separate shallow bowl. Whisk club soda into flour mixture until just combined. Pat crab quarters dry. Working in 4 batches, dredge crabs in cornstarch, shaking off excess. Dip into flour batter, allowing excess to drip off. Place in hot oil; fry until crisp and light golden brown, about 4 minutes, turning once halfway through cook time. Drain on a wire rack set inside a rimmed baking sheet.

Step 5

Using a serrated knife, split baguettes, cutting to, but not through, opposite side. Spread 2 tablespoons mayonnaise on cut sides of baguettes. Divide crabs evenly among baguettes. Spoon tamarind sauce over crabs; top each with 1/4 cup cilantro leaves and 1/4 cup pickled carrots and daikon.