Preheat the broiler to high. Line a baking sheet with a silicone baking mat or aluminum foil.

Prepare the bok choy by removing the thick root end. Slice each stalk into quarters, then cut into rough chunks. Set aside.

Pat the fish dry with paper towels and place on the prepared baking sheet. Spread 1 tablespoon of pesto over each fillet. Sprinkle 1 tablespoon of cheese over the pesto on each fillet. Season with pepper.

Cook the flounder under the broiler for 5 to 7 minutes, or until it has reached an internal temperature of 145°F and is opaque.

Meanwhile, in a large skillet over medium-high heat, heat the olive oil. Add the bok choy and garlic and cook, stirring frequently, for 5 minutes.

Remove the flounder from the broiler and transfer to serving plates. Add the bok choy and season with salt.