Place the mushrooms on a sheet pan and toss with 2 tablespoons of the sesame oil and the garlic, and season with salt and pepper. Roast for 10 minutes.
Meanwhile, whisk together the remaining 1 tablespoon sesame oil, lime juice, and ginger in a large bowl. Add the tuna and gently turn to coat. Season with salt and pepper.
Add the fish to the sheet pan, tossing gently with the mushrooms, and continue cooking for another 5 minutes.
To serve, divide the salad greens and cilantro between two plates and top with the mushrooms and tuna, drizzling any pan juices over the greens.