Rinse bok choy; trim off and discard tough stem ends and any bruised parts. Cut the leafy tops crosswise into 2-inch strips; cut the stems crosswise into 1-inch pieces.
In a 10- to 12-inch frying pan over high heat, stir garlic in 2 teaspoons oil until sizzling, 1 to 2 minutes. Add bok choy and broth, cover, and cook until thickest stems are just tender when pierced, 4 to 5 minutes; keep warm.
Meanwhile, rinse salmon, pat dry, and cut into 4 equal pieces. Mix sesame seed with ginger, and rub fish evenly with mixture. Pour remaining 2 teaspoons oil into a 10- to 12-inch frying pan over high heat. When oil is hot, in about 1 minute, lay salmon, skin down, in pan; cook 3 minutes. With a wide spatula, turn fish and cook until it is opaque but still moist-looking in center of thickest part (cut to test), about 3 minutes more.
Place salmon in wide bowls and spoon bok choy and broth equally around fish. Season to taste with salt and pepper.