Combine carrots, parsley, oil, salt, and pepper in a 7x11x2-inch microwave-safe baking dish. Cover with wax paper. Microwave at 100% power 5 minutes, stirring once.
To make an even thickness, fold over thin fillets or bend long fillets. Place fillets on top of carrots in the corners of the dish with the thick parts towards the outside and thin parts toward the center. Combine the mustard and honey and spread over fillets.
Cover with wax paper. Microwave at 100% power 2 minutes. Rotate fillets, placing cooking parts toward the center and continue to cook 1-3 minutes longer or just until fish flakes easily when tested with a fork. Let stand, covered 2 minutes. Arrange fish and carrots on 4 warm plates.
