Trim the crusts off the bread and set aside.
In a liquid measuring cup, whisk together the eggs, cream, sugar, soy, and mirin. If you want to go the extra mile, strain the egg mixture.
Divide the egg mixture equally between two shallow bowls and add one slice of bread to each. Let soak for 1-2 hours covered, in the fridge, then very gently flip and let soak, covered, for another hour to two.
When ready to cook, heat up a non-stick pan over very low heat. Add a touch of oil and add the custard soaked bread (let the excess drip back into the shallow bowl) and cook, over low heat, covered, for 8-10-15 minutes, until slightly golden on the bottom side. Gently flip and continue to cook, covered, until the other side is golden and the toast is puffy.
Serve and enjoy hot, either unadorned or with whipped cream, syrup, and powdered sugar, if desired.