Heat oil in a skillet over medium-high heat. Add tofu, mushrooms, broccoli, onion, and celery. Saute until just tender, about 5 minutes.

Mix soy sauce and cornstarch together in a bowl. Add mixture to the skillet with the tofu mixture. Cook until thickened, 4 or 5 minutes more.

Heat pita bread in a toaster until warm, about 1 minute. Spoon the tofu mixture into the bread; add Cheddar cheese as garnish.