Preheat the Oven – Set the rack to the middle position and the temperature to 400ºF (204ºC).
Prepare the Bread – Line a sheet pan with parchment paper. Place bread slices on the pan and use the back of a spoon to indent each slice's center.
Make the Custard Filling – In a medium bowl, whisk together the Greek yogurt, egg, sugar, cinnamon, and nutmeg until smooth.
Fill the Bread – Add about 2 tablespoons of the custard into the center of each piece of bread. The filling amount will vary depending on the size of the slice.
Bake – Cook until the custard is set and slightly wiggly on top, about 12 to 14 minutes. The custard should reach 170 to 175ºF