1. Preheat broiler. Brush a small baking sheet with some of the oil; set aside. Whisk lime juice, soy sauce, and honey together in a medium frying pan (not nonstick). Add fish, skin side up, and marinate 5 minutes.
2. Meanwhile, whisk together 1/2 cup broth, 1 tsp. miso, the mustard, and 1/2 tsp. salt in a small bowl; set aside.
3. Arrange fish, skin side up, on oiled baking sheet, reserving marinade in pan. Sprinkle cayenne over fish and broil 6 in. from heat until just cooked through, about 6 minutes.
4. Meanwhile, add mirin and remaining 1 1/2 cups broth to marinade in pan and simmer over medium heat until sauce is reduced to 1 1/2 cups, about 7 minutes. Whisk in sugar and remaining 1 tsp. miso and keep sauce warm.
5. Heat remaining oil in a large frying pan over medium-high heat. Add bok choy, leeks, and remaining 1/2 tsp. salt and cook, stirring often, until vegetables begin to soften, about 3 minutes. Add the miso-mustard mixture and cook, stirring occasionally, until vegetables are tender-crisp, about 3 minutes.
6. To serve, divide vegetables among 4 wide, shallow bowls. Add a piece of fish to each and pour sauce into bowls. Garnish with some daikon radish.