Place tofu in freezer 72 hours ahead of time. To thaw, fill a large saucepan with water and bring to a simmer. Leave tofu in package and place in water for about 20 minutes.
While tofu is thawing, heat 2 teaspoons vegetable oil in a small skillet. Saute onion and celery until soft and lightly browned. Place in a medium bowl and set aside.
When tofu is thawed, squeeze out excess water. Chop tofu finely and place in bowl with onion and celery. Mix in egg, cheese, salt and pepper until thoroughly combined.
Heat a large skillet over medium-high heat and pour in 1/2 cup vegetable oil (oil should be 1/4 inch deep). Drop tofu mixture into pan in 6 equal portions. Flatten with a spatula to form patties. Fry for 5 to 7 minutes on each side, until golden.