Fish With Rum Butter Sauce

Name: Fish With Rum Butter Sauce
Ingredients: 3 whole green cardamom pods, cracked; 1 3-long cinnamon stick; 2 tsp. whole allspice; ½ cup (1 stick) unsalted butter, room temperature, cut into 1 pieces, divided; 1 small white onion, thinly sliced; 1 3 piece ginger, peeled, thinly sliced; Kosher salt; ¼ cup spiced rum; 1 Tbsp. fresh lime juice; 4 4–6-oz. skin-on cod, hake, or haddock fillets, patted dry; 3 Tbsp. extra-virgin olive oil, divided; 2 cups cherry tomatoes, halved; Cilantro leaves (for serving); 2 layers of cheesecloth