Although it is one of the most popular species, tuna is tricky when it comes to sustainability. To make sure you're making a sustainable choice, buy U.S.-caught fresh or frozen Pacific albacore tuna. Fresh albacore is normally available only in the summer months.
Heat a medium skillet over medium-high heat. Add olive oil to pan, and swirl to coat. Add mushrooms, and saute for 5 minutes or until lightly browned, stirring occasionally. Add broth and vinegar; boil for 1 minute or until liquid almost evaporates. Keep warm.
Steam bok choy 1 minute. Heat a medium skillet over medium-high heat. Add sesame oil to pan; swirl to coat. Add bok choy, cut sides down; cook for 1 minute. Add soy sauce and sesame seeds; cook 1 minute or until thoroughly heated. Add 1 tablespoon bok choy cooking liquid and cilantro to mushroom mixture; stir to combine.
Heat a large cast-iron skillet over high heat. Add canola oil to pan; swirl to coat. Sprinkle fish evenly with salt and pepper. Add fish to pan; sauté 1 minute on each side or until desired degree of doneness. Let stand 1 minute. Cut into 1/4-inch-thick slices. To serve, place 1/2 cup rice on each of 4 plates; top each serving with 2 bok choy quarters. Arrange 1 tuna fillet on each plate; top each serving with 1/4 cup mushroom mixture.