Stir miso, mirin, sake, brown sugar and soy sauce in a shallow dish. Add salmon fillets; turn to coat. Marinate at room temperature, 10 to 15 minutes, or in the fridge for up to 2 days.
Preheat the grill and set oven rack on top rail closest to the grill.
Line a baking tray with foil. Transfer salmon fillets onto the tray, reserving marinade.
Place pak choi in the marinade; turn to coat. Arrange pak choi next to salmon on the baking tray, reserving marinade.
Grill until salmon is lightly charred on the edges, about 4 minutes. Flip salmon and pak choi; brush with reserved marinade. Continue cooking until salmon is browned and flakes easily with a fork, about 3 minutes. Transfer salmon to serving plates. Continue cooking pak choi until it is tender-crisp, 3 to 4 minutes more.