Preheat oven to 220°C. Whisk together oil, soy sauce, black bean paste, ginger, honey, and crushed red pepper in a small bowl.
Fold 1 (24x16-inch) parchment paper sheet in half, short side to short side. Open sheet, and place 1 cod fillet near fold in center of 1 half. Place ¾ cup snap peas, 1 cup mushrooms, and ¼ cup bell pepper on top of cod. Drizzle with 1 tablespoon ginger sauce. Fold other half of parchment over cod mixture; crimp all edges together with overlapping small folds to seal tightly. (Packet will be a half-moon shape.) Place on a baking sheet. Make three more packets, reserving remaining ginger sauce for serving.
Bake packets until fish flakes easily with a fork, about 15 minutes, carefully cutting tops open to allow steam to escape and to check doneness of fish. If needed, return fish to oven. Top with cilantro sprigs, and serve with remaining ginger sauce.