Step 1

Place 3 whole green cardamom pods, cracked, one 3"-long cinnamon stick, and 2 tsp. whole allspice on cheesecloth and gather up corners into the center; tie closed with kitchen twine. Melt ¼ cup unsalted butter, room temperature, cut into 1" pieces, in a medium saucepan over medium-low heat. Add 1 small white onion, thinly sliced, one 3" piece ginger, peeled, thinly sliced, sachet, and a large pinch of kosher salt and cook, stirring occasionally, until onion is softened but hasn’t taken on any color, 5–7 minutes. Pour in ¼ cup spiced rum, increase heat to medium, and cook, stirring occasionally, until evaporated, about 2 minutes. Remove saucepan from heat.

Step 2

Remove sachet from pan and discard. Transfer onion mixture to a blender and pour in 1 Tbsp. water. Purée until smooth. With the motor running, add remaining ¼ cup unsalted butter, room temperature, cut into 1" pieces, a few pieces at a time, waiting until incorporated before adding more; blend until sauce is smooth and emulsified. Add 1 Tbsp. fresh lime juice and a large pinch kosher of salt and blend to combine. Taste sauce and season with more salt if needed. Cover and keep warm in blender while you cook the fish.

Step 3

Season four 4–6-oz. skin-on cod, hake, or haddock fillets, patted dry, on both sides with kosher salt. Heat 2 Tbsp. extra-virgin olive oil in a large nonstick skillet over medium-high. Arrange fillets, skin side down, in pan and cook until skin is crisp and flesh is almost cooked through, 5–7 minutes. Turn fillets over and cook until flesh is opaque and flakes easily with a fork, about 1 minute. Transfer to a plate.

Step 4

Heat remaining 1 Tbsp. extra-virgin olive oil in same skillet. Cook 2 cups cherry tomatoes, halved, stirring occasionally, until blistered in spots and starting to collapse, about 4 minutes; remove from heat.

Step 5

To serve, spoon about ¼ cup sauce into each shallow bowl. Top with fish, placing skin side up, and tomatoes. Scatter some cilantro leaves over.