Break star anise into small pieces. In a 10- to 12-inch frying pan over medium-high heat, stir star anise or anise seeds, cumin, and coriander until fragrant, 2 to 3 minutes. Pour spices into a blender and whirl until finely ground, or pour into a mortar and grind with a pestle.
Add coconut milk to frying pan; stir often over medium-high heat until milk is bubbly and fat begins to separate, 2 to 6 minutes (reduce heat if milk splatters out of pan). Add all the curry paste and stir until aromatic, 2 to 3 minutes. Add 1 1/4 cups broth, ground spices, whole basil leaves, fish sauce, and sugar. Rinse kaffir lime leaves, tear each in half, and stir into sauce; set aside.
Rinse fish and pat dry; cut into eight equal pieces and arrange in a 12- by 16-inch baking pan. Drizzle oil over fish and turn pieces to coat; set slightly apart.
Bake in a 400° regular or convection oven until fish is barely opaque but still moist-looking in center of thickest part (cut to test), 10 to 15 minutes for halibut, 8 to 10 minutes for catfish.
Meanwhile, in a 5- to 6-quart pan over high heat, bring 2 1/2 to 3 quarts water to a boil. Add beans and cook until almost tender to bite, 3 to 5 minutes. Stir in bell pepper, then drain immediately.
Just before fish is done, stir green curry sauce over high heat until hot again. In a small bowl, mix remaining 1/2 cup broth with 2 teaspoons cornstarch. Add to hot curry sauce and stir until it boils and thickens, about 1 minute. If desired, remove kaffir lime leaves.
Mound hot rice on eight dinner plates. Lay fish on top and scatter beans and pepper strips around fish. Spoon curry sauce over and around fish. Sprinkle slivered basil over the top. Or serve fish, sauce, and vegetables on a large platter, with rice in a bowl alongside. Add salt and pepper to taste.