After cutting off the bread's crusts, set it aside.
Whisk together the eggs, cream, sugar, soy, and mirin in a liquid measuring cup. You might take it a step further and strain the egg mixture.
Spoon one slice of bread into each of the two shallow dishes that you have equally divided the egg mixture between. Cover and let soak in the refrigerator for one to two hours. Then, carefully flip it over and continue to soak for an additional hour or two.
Preheat a nonstick pan over very low heat when you're ready to cook. A small amount of oil should be added, and the bread should be soaked in custard (letting the excess fall back into the shallow bowl). Cook, covered, over low heat for 8 to 15 minutes, or until the bottom side is beginning to become brown. After giving it a gentle flip, cook the toast covered until it is fluffy and brown on the other side.
Serve hot and enjoy plain or, if preferred, garnished with powdered sugar, syrup, or whipped cream.